Seeking Feedback on a New Idea

     This year I'm going to get to go through a trial run of something new in our high school. As far as I know, it hasn't been done before in any school around here; it actually is something you'd see more in a college setting. I will be team teaching algebra 2 and pre-calc with another teacher. This isn't co-teaching in a sense that most teachers think about - I will be teaching these classes with another math teacher. Essentially what will happen is we'll combine our two classes (50-60 students in one room with two math certified teachers). My colleague and I are excited about this opportunity and knowing that it's never been done before, we are expecting both successes and failures as we go through this process.
     We started teaching across the hall from each other this year, and because of this, started sharing what we were doing in our classes. If I thought something went great, I'd share my excitement. If something went poorly, I'd ask his advice. He did the same. In this collaboration we realized that we had very similar teaching styles. We both have a desire to push our students to their highest level through problem solving. We also want our students to understand why all of this math works. The 'why' is the biggest part; we stress that more than anything. All of this produced the idea of teaching together. We were curious to see what we can do together in the same room bouncing ideas off of each other as the class progresses.
     We tried this is short bursts last year. We would poke our heads into each others' rooms during our planning and just jump in the lesson, adding our two cents when appropriate. It worked great because we were able to think of things that the other didn't. The students never knew who was going to speak (we didn't either) and because it was new to them, they were hooked. After doing it randomly without planning at all throughout the year, we asked the students which they liked better - one or two teachers. Hands down they all preferred the two teacher model. They liked the "structure" and they liked getting ideas and info from different perspectives. They also liked being able to get individual help. After these few lessons were assessed, their achievement was up (not that there was a cause and effect relationship).
     Together we loved teaching this way. I think we were able to learn from each other as much as the students were learning from us. Obviously we saw great potential in this style which is why we are pursuing it on a grander scale.
     However, I write this not to share my experience so much, but to ask a favor. We want to make this as beneficial for our students as possible. So I ask you: If you had the opportunity to teach with someone that you really worked well with (whether its in your building, or a fellow tweep, some make believe person you have yet to find, or a body double of yourself... or Dan Meyer) everyday, what are some things you would do in the classroom? How would you organize it? What could you do with two math teachers in 90 minutes for 50 students? We will be teaching algebra 2 and pre-calc, are there any specific topics that you could do some really beneficial stuff with? What are some challenges you foresee? How should assessment be handled? Literally, what are any thoughts you have with this? Do you think it will be a disaster, or do we have a chance?

For Real, Though. What's The Deal?

     I realize that this post is a little late, and Mrs. Fawn Nguyen has already beaten me to the punch, but I'll go for it anyway.
     Recently, Mr. Dan Meyer posted about an interview with Sal Khan in which this question was posted: 'What makes sports practice satisfying and how is sports practice different from math practice?' When questions like this are posed, my first instinct is to go to the source - the students. Since they are the ones making the decision, it would make sense that they could give us a straight answer right? I decided to put this to the test and ask some of my students. Below are some of the responses.

"I think kids are more up for working on sports rather than school because kids can actually see a physical change in their lives. more than just seeing a math problem and it being easier. plus you sometimes control how much more change you can see when its in sports."

"Alright, so this entire block I have been processing the question imposed with some deep thought. Yes, I do indeed have a brain. Shocker, right?! I think the answer that most teens would say is that you do what you are interested in. My personality is a good example! I don't enjoy participating in an activity or putting a great amount of effort into something that doesn't interest me. (It doesn't have to benefit myself for me to do it though. I ain't about that selfish life ;p) SO! Bringing this back to the question, sports practice is satisfying due to the fact that the student selected to do it, and it is normally a passion of the kid."

"Its definately an interesting article. The content is all correct unfortunately and I honestly don't know why I see it like that myself. My only theory on the issue is that it's easier to physically exert yourself than mentally exert yourself. Or in other words you would rather run 3 miles than solve a basic algebraic equation. There are 2 kinds of people, the ones who are scholars and the ones who are athletes, and sometimes there is a good mix. But, do you have a passion for Math or do you have a passion for Baseball? Would you rather get your Ph.d in formulas and theorems or would you rather get drafted into the Major Leagues? It comes down to passion, does that make any sense? It's either your passion or your just a whiner. XD Really interesting Mr. Brandt thanks for the read!"

     And one more...

"In regards to your inquiry, I am taking my quite valuable time to respond. In all due respect, my first thought was that most math taught is not applicable in the everyday life and thus a waste of time. However, upon pondering your attached article, I realized that my previous cognition was not valid. Math is an essential quality of our lives. We use it with out even giving it a second speculation. Though I have stated one of my opinions, I, in turn, have not addressed your main question.
Sports practice and math class differ in that one is an extracurricular activity while the other is an intellectually involved course. The descriptions above only graze the surface of the in depth reasoning to sports practice being more enjoyable than a math class. Sports, are a freedom that you choose to participate in that differs from math which you are required to partake in. With that statement, it is my belief that many students as well as me, feel that because math is mandatory we are derogatory towards it. We didn't sign up for it so why would we put forth an effort.
In another context, to me sports practices are more satisfying due to the belief that participants get more out of it. On the other hand, their is no way to measure these two oppositions to accurately compare them thus rendering my above statement vulnerable to critique. Sports are a great activity in which to get in shape, become a team worker, and learn beneficial life lessons. However, math provides us with knowledge and the ability to use that intelligence to succeed in the real world. Whom is to say that one is better than the other? While students tend to lean towards sports they must also realize the importance of mathematics.
So, to wrap up, students would rather participate in sports because they think they get more out of it and it is "fun". Were as math is a pointless burden to them"

      So, ideas - instant reward, interest, passion. Now I did not send this to all of my students, so this isn't exactly a good sample. I chose students that I have this year that are dedicated athletes and in good academic standing and that I thought would take this seriously. I sent it out to about fifteen different kids, but only received back four responses, so there is that too.
    To be honest, this is about what I expected to hear back. Everyone gravitates towards their passion and interests. Even if they don't have that part of their life figured out, they will figure it out by moving towards what they find fascinating. Also, as we know, students are all about their immediate satisfaction. Heck, I'm the same way. I've gotten better with age, but it is still difficult for me to stay motivated on something when the only goal is long-term; even in those cases I try to get it done quickly so I can see the end result.
     I was surprised, however, to see the slight confusion in their responses. Even the students themselves are not 100% sure as to why they gravitate to sports instead of school. Perhaps it is something that they haven't really thought about themselves but it just kind of happens. I'm sure if I got all responses back there would be more reasons based on the students' personal connections as well as some reinforcement of the above.
     In the last response, I found the phrase "...because math is mandatory we are derogatory towards it" interesting. Is this a reflection on how education is organized? Rather than educators seeking students' interests and teaching the content through those avenues, we are teaching content because of state tests. We are assigning grades based on 'student performance' instead of assessing them based on true mastery, which causes them to care solely about the grade and not about the content. If students had the option of taking various math courses based on where they saw themselves in the future, would the enjoyment factor go up? If art students took geometry because it's applicable but not algebra 2, would we see an increase in interest in math? Or is there still an overarching feeling that math is lame, difficult, and useless that will never go away?
     I could continue to analyze these responses, but I am curious what everyone else thinks. Leave some comments, provide some insight. If I get any more responses, I will post them.

Seeing Things Differently

I hang out with English teachers too much; I find myself searching for meaning in everyday events when before I just took them at face value.

Yesterday I was speaking to a colleague about how teaching is changing, not with technology, but with more exploring and student directed discussions. When I read about successful lessons/teachers, they are always ones that give students freedom and ownership, very student-centered. These lessons show how the math works, where it comes from, how it's connected to other areas, and what cool things can be done with it.

I went to school where the model was teach, examples, practice. Because of this, I grew up being a terrible independent thinker and problem solver; I had to teach myself these qualities in college. I graduated high school being able to only complete problems that I've seen carbon copy examples of. I do not wish this experience for any of my students, and I believe many good teachers agree.

I had to learn (and still am, everyday) how to organize lessons focused on my students on my own. My undergrad work too was more teacher-centered than I would've liked, as was my student teaching, and there was never any criticism for it. It makes me wonder how colleges are training future teachers. How they changed with current, effective practices or are they still training in the same old fashioned way?

Our conversation continued with this and we ended it being positive about the future of teaching practices and slightly negative about some current practices. I left to go make some copies and in the machine I found a copy of the poem 'When I Heard The Learn'd Astronomer.' I've heard this before but never thought about it in depth. However, after the conversation I just participated in, I stopped and reflected. This poem describes what's currently going on in math education. We've got some really knowledgeable teachers that are showing facts and step-by-step processes, but they are not effective because they are not engaging their students. There are no connections, nothing interesting for non-mathematicians to grab on to, just straight facts. Math has a stereotype of being challenging, boring, and just for nerds, and that's really not true at all. Just like any subject it can be accessible to all students as long as it's presented in the right way.

I often read through my twitter feed and various blogs and wonder what it would be like to teach in a school with everyone I follow. I'm constantly reading so many great ideas from teachers that get it and are constantly striving for perfection and challenging themselves. I wonder how successful a math department of this caliber could be. I would love to participate in professional development opportunities with them to engage in conversations that are longer than 140 characters. To work with teachers that share this common goal, that is the dream. When everyone's heart is truly at the right place and they are doing what is best for their students, mastery happens, and with that independent interest grows. And that is where the learning occurs.

When I heard the learn'd astronomer;

When the proofs, the figures, were ranged in columns before me;

When I was shown the charts and the diagrams, to add, divide, and measure them;

When I, sitting, heard the astronomer, where he lectured with much applause in the lecture-room,

How soon, unaccountable, I became tired and sick;

Till rising and gliding out, I wander'd off by myself,

In the mystical moist night-air, and from time to time,

Look'd up in perfect silence at the stars.

- Walt Whitman

Leaves of Grass, 1900

emphasis mine

Quadrillions of Pennies?

     The other day, a colleague of mine and myself were discussing exponential growth and how to open this to his students. I've never taught it before, so I felt that I wasn't the best person to ask but thought I could learn something as well. He suggested the classic problem of 'would you rather have $10,000 now or one penny today, and twice as many pennies each day for a month.' I thought this would be great, and I mentioned the similar problem of if you have a bean on the first square of a checkerboard and you double the number of beans for each square, how many will you have on the sixty fourth square. He decided to go with that instead, but use pennies instead of beans. Long story short, his students were amazed at the fact that there would be 92,233,720,368,547,800 pennies on the last square, not to mention the total amount of 184,467,440,737,095,000 pennies on the board.
     Needless to say, both of us were also shocked. In my geometry classes, I've been trying to take our calculated values and putting them into a context that students can relate to. Saying that a box has a volume of 150 cubic feet means nothing to a student until they can see what one cubic foot looks like. So having a value so large was just that to his students: a large, inconceivable number. We tried to put it into a context that was relatable but we kept coming up short. Nothing that we did, relating it to the dollar amount, distance, etc. made sense to us or our students. We came up with one good comparison, but it still wasn't the best.
     I decided to use this as an opportunity to experiment. As we were discussing the number I had students in my room taking a test. We were speaking just about the numbers but did not mention the context. One student looked at me afterward and laughed saying, "You guys are such nerds, talking about big numbers." I went on and on about how cool it was for the answer to be that big, and then I realized he had no idea what I was talking about. I described the original problem to him, and he became interested. I then put it into context, saying that's like if you stacked pennies on top of each other, that stack would reach Pluto from Earth 1,911 times. His response: "Wow," and then he pondered. I could see the look on his face, focused on what I just described to him.
     Subject #2 conversation went like this - Student: "Mr. B what's this large number on your board?" Me: "Go ask Mr. Miller, he'll tell you." Student comes back: "Yeah, he said something about pennies and checkerboard. I wasn't really paying attention." Me: *describes problem* "That's how many pennies would be on the last square." Student: "Ok." Me: "That's like if you stacked all of the pennies on top of each other, that stack would reach Pluto." Student: "Woah. That's awesome." Me: "955 times!!" Student: *mind blown*
     I type this because context matters. I've tried this discussion with many other students and the response was always the same: they start out not caring but then are super interested when they are able to relate to what is going on. Now, I understand that there are some math problems and topics that can be engaging in the pure form that they are. I'm not saying that everything has to be taught in a real-world context. However, students need to be engaged and they need to have a reason to be engaged. I do not like when entire courses are taught without any context whatsoever. How does this help students? In my opinion, this helps to create students' hatred of math. They don't have a reason to care about it so they don't try, which results in them not succeeding, which results in anxiety, and the cycle continues (well, perhaps that's an exaggeration, but it certainly does not help). I want everything I teach to be engaging and relatable, whether its connected to the real-world or previous topics we've discussed. Nothing should be so abstract that they can't comprehend what's really happening. I believe math can be interesting to all students, we just need to figure out how to get them hooked from the beginning and everything we can to keep them there.

Am I Really Making A Difference?

     The other day I was talking to a colleague of mine and the following question came up: 'Does what we do really make a difference within our students?' This question, while it was supposed to be part of a short conversation, quickly turned into a meaningful discussion that has got me thinking about what I do in the classroom and the true, long lasting effect I have on my students (if any).

     The department member that I was engaged in a conversation with has a very similar teaching style to my own, one of which I believe is gaining popularity in the math education world - a style of inquiry-based, student-centered education. We both pose challenging problems to our students and use them to investigate new topics; keeping the students engaged with the material by giving them tasks that are just out of their reach, keeping them thirsty, and illustrating the connections that exist within mathematics. We've both had great success with this style, and its apparent by the students' comments and interest that traditionally has not been seen in past math classrooms. Throughout my department, I am trying to push this style and encourage my fellow colleagues to step out of their comfort zone and give their students some freedom and control of the classroom. The times that I have heard of them trying this, they have reported success, but I'll be honest, as the department facilitator I'm not entirely sure as to how much this is happening in our classes. Is it occurring on a regular basis? Are the majority of my department members doing this? Do most students see standard, old fashioned lecture-style lessons straight from a textbook throughout the majority of the high school careers? I have my thoughts, but nothing based on fact. This 'unknowingness' tells me that I need to get into other classrooms more. I need to observe what's happening in my department so that if our students aren't achieving what they should, I can locate any possible issues. With these thoughts running through my head, and with the conversation I had yesterday, I've been wondering if my students really are different at the end of a semester with me, and if they are, does that change last or get reset?
     In talking with my students over the years, they have mentioned that they enjoy my class and my teaching style because they see the connections and are forced to work to their potential; they learn to problem solve instead of regurgitate and they become critical thinkers instead of machines (well, most of them). I can see this develop in them throughout the semester. As far as concrete, data driven evidence, I'm not sure I have any, but I can witness the growth. My fear is that when they move from my geometry class to algebra 2, do they become the student they used to be, or do they continue to approach math in a new way? If their new teacher does not challenge them, do they lose that ability to think for themselves? And if so, can they bounce back if they get a teacher that can push them, or do they need to be 'retrained' (I don't really like that word for this context, but can't think of anything better)?
     Ultimately this conversation led to us being fearful that our students go back to their old habits and what we've done with them is almost a waste. I hate to sound so negative, because I certainly do not think that what I do with my students is a waste, but if there are no long term benefits then I don't know how else to think about it. Throughout the semester I try to build my students up to a point where they are not afraid to attempt any problem and they can be proud of the work they complete, even if its wrong. If they move on to a class where all of the information is given to them directly and all they need to do to be successful is follow an example in a textbook, then they are not being challenged and they realize that their work is not valued. They may not have to try really hard throughout the entire semester and could still get an A. And worse, if they then move to a class that challenges them again, then they are back to their old routine. This, of course, is what I'm worried about and I'm still trying to figure out if this happens or not.
     As the department facilitator, I know that it is my job to get all of my department on board with challenging all students and getting them all engaged in the material, for all courses. With new teachers, I think this is easier to do than with older, more experienced ones. Especially today, the trend seems to be for teachers to be introduced to this "new" student-centered style. However, teachers that have been around for a while, as we know, are more likely to stick to their old habits and come up with many excuses/reasons to not change. I'm speaking in generalities at this point. My department members have seemed to be open to new styles and tools that can be used to effectively teach their curricula, but there may be some that just aren't sure how to do it. If there are teachers that focus on what is only in a textbook and need everything almost scripted to teach, how can that be changed?
     I believe that in my department we need to be more consistent in how we teach. Obviously we all have our own individual styles for delivering information - I don't want to completely change everyone. However, getting back to my original question, I do want our courses to all have a certain level of rigor so that students feel challenged and interested in every course they take and they don't have to worry about what teacher they have next year. Maybe this is too idealistic, but it is a goal of mine. I don't want students to have to beg for one teacher because they are easy or because they are tough, or cross their fingers that its not so-and-so because of stories they've heard from their friends. I want consistency in the quality of education that will be provided to all of our math students. As a teacher, I don't want to be torn between filling in knowledge gaps for half of my students because they had one person and continuing at a certain pace because the other half had someone else.
     As I write this, I realize that I've gone down a bunch of different roads that I didn't expect all because I want to know if I change my students in the way they problem solve for the better. It boils down to this: I want the comfort of knowing that what I do is making a difference or the frustration knowing that I need to change to make that happen. Right now I'm somewhere in the middle. I'm not exactly sure how to get an accurate answer to this question, which is quite disheartening. Ideally, I could have the same group of students two years in a row and see if what I've done has stuck with them. But even that wouldn't tell me if my strategies continue when they leave my room.
     Of course, there is always the possibility that my students are just telling me what I want to hear, and they really do not like how I teach at all. Crap, that's a whole different set of issues...

New Year, New Idea

I watched Mr. Cornally's TED talk, and immediately wished I worked in a school that operated the way he described. If you haven't watched it, please go see it before you do anything else. If he ever starts his own school, I want to work there. I shared it with some of my colleagues and even some of my students, and everyone responded with the same positive attitude saying it would be awesome to be able to get excited about education. The students that watched it expressed their love for studying something that they wanted to explore. This is what creates life-long learners and quality education. So, after much thought and reflection, I've decided that I'm going to start a little project similar to what Mr. Cornally described. It might be a lot of work, but it's going to be fun.
Some background info: In my school, we have what's called and 'iSpartan' block. Essentially it is about one hour of time where students are in their homerooms and they are expected to be working on assignments that teachers have provided. These assignments are meant to be ones that support and enhance current material and not just extra homework. During this time, students are also allowed to travel to their teachers to receive remediation if they have below a 70%. This block of time and policy is new for this year, and after watching it in action for one semester, I've noticed that many of my homeroom students either have not been assigned work or do not complete it in school (they wait until they get home or don't do it entirely). I do not like watching students do nothing during an hour of the school day when they could be using this time to their advantage. For my homeroom students, when they 'have nothing to do' during this time, I'm going to have them complete an independent research topic of their choosing. Below is an outline of what I've come up with so far. It is only a draft and needs some work, but it is what I've thought of off the top of my head. If you have any thoughts as to how this can be improved, please let me know. This is the first time I'm doing this and (as far as I know) the first time anyone in my district is pursuing anything similar.

----------------------------------------------------------------------------------------------------------------------

iSpartan Independent Project

Purpose: To allow students to explore any topic of their choosing in any way they desire. The bigger picture – to explore your creativity

Who: Homeroom students, Spartan tributes, select faculty as needed

Requirements: Do something interesting that exercises your creativity and pushes your limits, forcing you to dive deep into the material at hand.

                Create a presentation to share with the class that accurately explains what you did with great detail

Procedure: Students will come up with a subject, project, topic, etc. that they are deeply and personally interested in and will share with me. Together, we will communicate on how to make it specific and engaging to develop a product that they can share with the class. Students will work on their own, with help from a faculty mentor as needed, throughout the course of the semester to create this end product. Some work may have to be done outside of class. For students who are having trouble coming up with an idea, I will work with them to discover their interests and from that develop a topic to explore.

Timeline: Projects must be completed and presented to class before the end of the year. Students will sign up for presentation dates as they arrive at the end of their project. When students are close to finishing, they will meet with me to ensure that they’ve got into great detail. Students may explore more than one topic if they wish depending on time.

Ideas     : English - Write poetry, short story, screenplay, Snap Judgement-type stories, film original movie, book report, research paper (avoid if possible), organize flash mob and explain purpose/explore effects that it had (http://improveverywhere.com/)

                Science – build model rocket, Arduino electronics (http://www.projectallusion.com/1/post/2010/7/musical-handrail-using-the-mux-shield.html 2:00) (http://www.instructables.com/community/Piano-StairsFloor/), invent something, photography, robotics

                Arts – drawings, paintings, etc. that share common theme, write music/album and explain meaning, learn to cook something awesome, build something awesome and huge out of legos, www.songreader.net

                Math – physics, find math in something you enjoy, explore topic to its fullest, learn subject we don’t offer

                History – research historical event, reenact historical event, interview someone, go to museum/fieldtrip and report on what learned, have class take part in reenactment, film documentary

                Explore How Stuff Works, How Stuff Is Made, How To Do Anything

                Organize Event

Resources: Snap Judgement, Radiolab, TED, www.popsci.com/diy, 

Thoughts On Student Directed Curriculum?

WARNING: Lengthy, lack of visuals/humor. I'm going to hit you with some knowledge here (and I hope you, in turn, smack me with some feedback as well).

This is my sixth year teaching geometry and I'm pretty much at that point where I can walk in to my classes ask them what we talked about yesterday and I can go to town. I've always wanted to be at this point in my career, where I can spend time focusing on increasing the quality of questions and researching new ways of teaching rather than taking a tremendous amount of time just figuring out what I'm doing the next day, creating problems, etc. Because I have most of the ground work laid out, I've been able to try some really cool (and some not-so-cool) things over the last few years. For some of my units I've gotten rid of tests and created projects, for some I've made them more discovery-based and student-directed, and for some lessons I've created some really involved questions that require some incredible thinking from my students to solve. This year an idea I've been toying with is the student-directed curriculum. Its got some pros and cons to it and I'm not quite sure what I'm going to do.

Our geometry curriculum used to be like almost every other math class: follow the textbook. Unfortunately, we have UCSMP which is terrible in my opinion. When I rewrote the curriculum two years ago I had one goal in mind: organize it in a way that will make sense to the students and where connections can be made. I got tired to teaching topics and having to jump all over the place to struggle to draw the lines between everything. The beauty of geometry is that is all related and our students were not seeing that. Now, even though technically we jump all over the book (although no one in our dept uses the book anymore) I've noticed student achievement go up and we've been able to create deeper questions. The students don't care that they don't have a book to follow because the way that its organized makes sense to them. They would rather reference pg. 18 and pg. 262 in the same day than have everything disorganized and all over the place.

This semester I took the first three units (basic vocab, quadrilaterals, triangles) and mashed them together as opposed to teaching them separately. Now these units include things like all of the types of angles, symmetry, trig., and more, so they're pretty heavy on material, but I wanted to have it make even more sense for my students (if that's possible). As I thought about the curriculum, I realized that it could be organized in a number of different ways and still emphasize all of the interconnectedness of the world of geometry, but how could I have it be the absolute best for my classes? Or for anyone's classes for that matter?

 I started the year by asking my students what came to their minds when they thought about geometry. Their response: "Shapes and stuff." Me: "Name some shapes." Them: mur mur mumble mumble shapes blah blah ...and somehow I took it from there. I took the shapes they gave me and we started to dissect each one individually, exploring all the properties until there was nothing left to talk about, making connections as we went. I never had to say "Ok, we're done with that figure. Let's move onto the next one." because the properties naturally lead to more figures. Through student questioning I was able to completely cover the curriculum, plus some more.

Because this was my first time trying this, I limited myself to just the first three units as opposed to attacking the entire course this way. I'm teaching two sections of geometry and my hope was that I would be teaching them different concepts because their questioning would lead them to different places, but they'd end up at the same place in the end. I'll be honest, it got confusing. I no longer could stand in front of them and say "What did we do yesterday?" because I couldn't remember everything we'd discussed. I found myself keeping an unnaturally large number of post-it notes on my desk reminding me of what I've discussed with each class. I'd imagine when my third block asked my second block what to expect in class, they were surprised when they did something completely different.

I noticed that teaching this way caused achievement to increase compared to other years. Now, obviously I could just have an awesome batch of students (which I do), but I believe the way I taught had some impact as well. All of this has led me to ask myself, what if I taught the entire course this way?

Teaching an entire course through student questioning: innovative or something I should've been doing all along? Either way, there are some definite benefits and challenges to this approach. I believe my students would see some great success both in learning the basic knowledge and developing some higher order thinking skills. Teaching this way allows me to easily pull all kinds of topics together and potentially create some really cool projects. It would allow my students to really understand that math is all connected; its not separated into Alg 1, Alg 2, Geometry, Pre Calc, etc. but they're all based upon each other. It would also keep my students involved in the course. They would have complete ownership over the material because they would be determining what happens next. This also reinforces my philosophy of 'teach what makes sense, not what comes next in the book.' Looking through the PACCSS, I think I could hit everything with this style.

The tough part is that I have to almost be fully prepared to teach the entire course at any moment. Because I won't know where my students will lead me, I need to have everything ready to go on the first day. I'm sure I could predict a little bit as to where they would head, but I wouldn't know what they're going to do on a daily basis. If I taught this way I wouldn't want to push them in any direction unless they stall; I want them to be pushing me. Another challenge is keeping straight what I've covered and what I haven't in each class. If I would do this next semester, I teach three sections of geometry, that would be three different places in the curriculum simultaneously. I would be very fearful that I would forget to cover something or I'd start going over something in May that we discussed in February. While ideally this would be 100% student run, obviously there would have to be some questioning on my part to push them, which would give me some influence as to what's being discussed. My post-it note system of organization would fail rather quickly and I'd have to come up with something more efficient. I'd also need to create a new system for catching students up when they are absent. Maybe designate someone to constantly take picture of the board and post them online? There are some details to figure out.

As of now, I'm leaning towards doing this for one class instead of all three as a trial. This might help me get some of the details worked out before I push through entirely (of course, we all know what will happen if I do this: this will be the last year I teach geometry and I'll be back to the drawing board with new courses next year). It would also be fun to switch things up a little bit. I'm excited, and scared out of my mind, to try this. I'm not usually the most organized person in the world so this plan has potential to fall apart in a hurry. I'm hoping my desire outweighs any negatives that would potentially come out of this. The positives definitely outweigh the potential bumps in the road, and because of that I keep coming back to "I'd be an idiot not to do this!" I can't help but think of a quote from Mr. Pershan that I recently saw on Twitter (@mpershan), "If I'm not working really hard - if it isn't mentally exhausting, then I'm probably not getting better."

However, this style does kind of go against the 'common unit assessment' plan that my district has implemented for this year. Having common courses among teachers gets thrown out the window with this idea. Oh well... I gotta do what's best for the kids.

Do you, Mr. or Mrs. Reader, have any thoughts on this plan? Any positives or negatives that I didn't mention? Any ideas on how to overcome the negatives?

Go Team! Teaching

It was a cool Monday morning; students were trudging through the building as if they were just rolling out of bed and trying not to fall down the stairs. I was huddled at my desk trying my best to prepare for the day and change the lives of my students. The sound of squeaking shoes and muddled conversations was beginning to break my concentration. I tried to push through, but soon realized that it was no use; time for my morning duty. As I stood in front of my classroom door, I could now put faces to the growling sounds coming from the hallway. I did my best to transfer my energy for the day to my past and current students. I even transferred a 'Good Morning!' to those that I did not recognize, but alas, no results. As time ticked away, a fellow colleague of mine stopped by my room to ask a favor. He had a meeting during his first block class and asked if I could cover for him for a few minutes. "No problem," I said, "what are you teaching today?" He responded with, "The students are learning about function operations. I'll leave options on my desk for you if you don't feel comfortable teaching a lesson." He handed me his notes for me to look over if I was interested in teaching, and I thought to myself "Sure, I can do this on the spot." During homeroom, I read over his notes, quickly trying to come up with something interesting and engaging that I could present to his students. I had no interest in 'out-teaching' him in any way, I simply wanted to put together a quality lesson. I certainly did not want to take away from his class in any way. Fast forward 15 minutes and I'm standing in his class getting ready to teach. I was given the option to allow them to continue their classwork, go over their homework, or teach. I was feeling confident in teaching, and I recognized half of the students from previous years, so I went for it. I began teaching function operations and function composition to a pre-calculus class that I had never planned for before and it went Xtremely well. While there wasn't much exciting to the lesson, I was able to build off of their prior knowledge and construct new ideas that stuck. However, the best part was yet to come. About 10 minutes into my teaching, my colleague returned to the room. Since I was in the middle of a thought, I continued until I came to a stopping point. I asked if he wanted to take over and he sat down and let me continue. No problem; I was having a grand ol' time. It was a unique experience teaching a lesson and having the students participate and listen 100%. I'm used to freshmen that are still all over the place and seniors that have a hard time understanding the value and beauty of mathematics. These juniors were on top of their game and begging for more information. It didn't take my colleague long to notice this (he experiences it on a daily basis with them) so after a few minutes he jumped right in, helping me teach. Before I knew it, we were both teaching his students, and they were hanging on every word. We were able to bounce concepts off of each other, fill in gaps where one (me) might have missed something, and fully illustrate what function operations really represented. As the students led me through examples, he was standing at the smartboard illustrating what was going on through graphs. I noticed the students' heads constantly moving back and forth, but not in an overwhelming way. They were truly engaged, hanging on our every word. Jokes were told, knowledge was passed, lives were changed. I
In talking with my colleague the next day, he said his students remembered everything we had talked about in the previous lesson. Team teaching was effective, and super-freakin'-fun! He said the students loved it and requested that it happen again on a regular basis. I walked in later in the week and I could see the excitement on their faces grow, not because I'm awesome, but because they were hoping to have some more fun in math class! Fun in math class? Really? Is that possible?
I've always heard of team teaching and thought it was something that was only done in the past. But now I know why it was done, because it works! The lesson we did together was completely spontaneous and I think it was one of the most effective lessons I've ever been a part of. Just think of what we could've done had we planned it out ahead of time!?! So, obviously, we've decided to make this a regular part of our lives. Because of the positive outcome, we're going to get together and plan lessons and be guests in each others' room at least once a week. But doesn't that cut into your planning period? Yes. Doesn't that make you so mad? No. Aren't you going to ask for extra payment since your teaching more? No. This is fun, and its great for the kids. A better question is, why wouldn't we do it??
As we do this more, I'll try to get some pictures and post updates as to how it is going. I believe this week students will see more than one teacher in their room, but not for intimidation purposes...

Sir Ken Robinson

Last night I had the amazing opportunity to watch Sir Ken Robinson speak at Millersville University. I left speechless. If you are unfamiliar with his work, please go here and here and here.
There are so many thoughts running through my head at the moment I'm not exactly sure I can write anything that will do his talk justice. I'm wishing I would've wrote this post last night when I got home instead of sleeping. I do want to highlight just a few points that Sir Ken made that stuck with me and will cause me to rethink my classroom and department.
1. How do you run an organization that is adaptable to change and flexible? One that is creative? One that keeps up with change and stimulates change? Public education needs to be this way. One point that he made, and that I agree with, is that schools are all about conformity. All students take the same classes at the relatively the same time and are expected to get the same grade. Schools need to allow students to explore their interests and creativity so that they can find their element. This will require schools to adapt to the students it educates rather than the students adapting to the schools they attend. There are many steps that need to be taken for this to happen, and its certainly not something that will happen overnight. Can we as individual teachers do anything to support this process, even if the governing bodies do not officially embrace it? Sure.
2. NCLB is actually leaving everyone behind. Standardized testing is causing teachers across the country to mold their students into machines, learning processes but not thinking about what is going on. Usually, this is done in the most boring way possible. When students are looked at as data, they revolt. When they are looked at as individuals, they succeed. A political policy that was supposed to help education and increase our students knowledge is, in reality, taking away from their education because they are being forced to learn about things that they see no value in. They are not able to express their creativity because they are limited to what's on the test. Combine this with the decrease in public education funding and you lose those courses that engage students and stimulate their creativity and you keep the courses that are cut and dry.
3. We are reducing our funding for education increasing our funding for the correctional institutions. 1 in 31 people are in, waiting for sentencing, or being rehabilitated by a correctional facility. Not that those two statistics are directly related, but its interesting to think about.
4. Personalizing education helps people realize their talents. Every attempt to personalize education has failed. Standardized tests de-personalize the educational experience. This was really the subject of his entire talk.
5. By narrowing the curriculum, we are implying that life is linear; that we all will follow the same path. In truth, life is organic; its constantly changing and adapting to surroundings. Let's teach our students how to make these adaptations rather than telling them what to do and where they should be. Let them discover what they are good at and what they are interested in, and let's foster it. If we tell them what to learn and how to learn it and don't move off of the curriculum that is set for 'everyone,' how will they ever learn their place in life? There are plenty of people in the world that are good at what they do, but don't truly enjoy it. Let's have our students graduate ready to pursue a career that they are good at AND love.
6. Myths - 1. Only special people are creative. 2. You are either creative or your not. 3. Special things are required to be creative. 4. You can't teach creativity.
7. As teachers, we are like gardeners and our students are our plants. Gardeners don't grow plants; plants grow themselves. Our job is to provide the optimal conditions for growth. Beautiful analogy.
8. The risk we take in margenalizing our students is greater than the risk of letting them be creative and grow.
9. "I'm not what's happened to me, I'm what I chose to become" - Carl Young

Of course, these are not my original thoughts. They are all from the great Sir Ken Robinson. He said so much more and was extremely informative and insightful, but these are just a few of the points that stuck with me and will guide my classroom from now on.

Lil' Help

I need some guidance, help, advice, etc. The first unit in my geometry class was big on vocab to set the pace for the rest of the course. It focused on all of the different types of angles, polygons, and quadrilaterals. We explored each to their fullest, expanding on and making connections to every characteristic possible. In the past I've given an exam with problems and the students have done fine. Recently I started giving this as a quiz instead...

My students have to find all of the angles that I've labeled (36 of them total) in this regular dodecagon. I give them one right angle, but that's it. They need to find everything else on their own. I like this because they need to use the properties we talked about throughout the unit to arrive at the answers. Its a nice, different type of assessment that gets them to apply their knowledge.

I'm having trouble because I don't know how to grade it. Obviously, if they get one angle wrong that is going to through off other angles as well. I can't take points off for every wrong angle because then I'm potentially subtracting points for the same mistake multiple times, which isn't really fair. I need to find a way that assesses them fairly. I've thought about having them write an explanation of how they arrived at their answers, but that would be a ridiculous amount of writing, even if I made a simpler figure with less angles. I've also though about having them list their answers in the order they calculate them so I can try to follow their thought process, but I'm not sure if that would give me the full picture of their understanding. 

Could I evaluate it in some type of standards-based grading system? Are there any other ways that I could use this to assess my students, or do I just simply not grade it but make it a class activity?

Lil' help?

Note: as I type this I'm listening to the Dark Knight Rises soundtrack and I'm now totally pumped to teach for the day, although my lessons may be slightly darker than usual.

Student Directed Curriculum (kind of)

I teach geometry. This is my sixth time teaching it. I think I'm the only person in my department that hasn't changed what they've taught for the past six years. The perks: overall, less planning! The downside: more planning? trying to reinvent the same material so it doesn't seem like the same old thang, while still keeping it effective and relevant for the students.
I always push for questioning in my class. I do stand in front of the class and explain some things, but their questioning fills in some of the holes and also covers the curriculum. In the past, I've followed the set curriculum I helped to write a few years back. Just like any other typical class, I started at unit one and plowed through to unit 13 or 14, following the lessons in the order they appeared. I thought I would try something new this year: let the students decide.
My plan is to start with unit 1, the basics of geometry (terms, notation, polygons) and go from there. I have a paper that I made up with all kinds of lines on it and I provided three or four angle measures. With this, I'll let the students calculate as many angles as they can and find as many polygons as possible in 5 or 10 minutes. From there, they can share what they've discovered and we'll discuss in great detail everything they bring up. For example, if a student give me an angle measure, we'll talk about whether or not its correct and why its calculated that way and how it will lead to other answers. If someone points out a polygon first, say a kite, then we will explore every aspect of kites (angles, segments, symmetry, area, etc.) before we move on. Theoretically, the entire beginning of the course will be based upon this one worksheet. Unfortunately, I don't think I'll be able to give them complete freedom and follow wherever they lead me (not sure its physically possible to be that planned out) (now that I think of it, in order for my students to 'run' the curriculum, you would think it wouldn't require much planning since I'm not doing the work, turns out it might require more, hmmm...).
The downside is that my two geometry classes will potentially be at different points in the curriculum all the time. Its probably going to be tough to keep track of what I taught and what I didn't. The upside is, the students are thinking, their guiding themselves, we're working together, they're engaged. Now, as I type this a question arises, how do I handle assessment? I'll need to provide a certain amount of structure for this to work so it doesn't turn into complete chaos. Do I still keep the unit in the same order so as tests/projects can be used consistently between classes? I realize the exams should not be the motivation for such a decision, but how else would I handle it? If I let the units get criss-crossed and the previous order changes, do I allow it and move to project based assessment instead of exams? Or, do I simply evaluate when enough material is enough and write up new assessments, different for each class?
I probably should've thought this through a little more before the second week of school. Oops.

With A 'Lil Bit O' Algebra

So, I've recently been asked to rewrite our districts Algebra 1 curriculum (and eventually Algebra 2 I believe) to fit with the Common Core State Standards, again (woot!). Teaching something because the standards tell me to bothers me as opposed to teaching something because its relevant, but that's a rant for another time.
A colleague of mine and I were looking over the CCSS for alg. 1 and realized its kind of a hodge-podge of topics thrown together. I mean, all of the linear equation/function stuff works together very well, but then there is some beginning stats/probability and also rational expressions, polynomials, exponents, etc. thrown in as well. We were trying to find a way to organize this course so that it makes sense and there are logical transitions. As of now, the topics are taught in the order in which they appear in our textbook (UCSMP), which is no good (both the organization and the book). We stared for a while and threw out some ideas, and then I realized something. Every alg 1 curriculum that I've ever seen has always ended with stats topics, and they are part of the 'if there is time' category. I wanted to give this course some flow and a context, so I thought 'Why not teach it from a statistics perspective?" After looking over the standards again, we figured out that this just might work. Here's the tentative plan:
      We'll start off with calculating different types of probability. This covers the different types of numbers, how to order them, represent them, compare them, etc. We will then move on to different ways to represent data, bar graphs, pie charts, stem and leaf, box and whisker, etc., further emphasizing the importance of number sense. This leads nicely into scatterplots and line of best fit, which opens a door to teach all of the linear equation/function topics that are essential to an algebra 1 course. This is obviously a very loose description since I don't have all the info in front me, but I think it will work. Every topic will have a context and we'll be able to teach everything in a real setting. My hope is that this allows students to see how these can be used and provide an easy method to be taught. I'm very excited for this to happen and can't wait for the results. It makes me wonder why I've never heard of anything like this before.
      The only hicup - the rational expressions, polynomials, GCF, LCM, exponents topics that are to be included. How do we incorporate them into a stats context that flows well with everything else in the course? As we talked, the best we could come up with is 'throw them in at the end.' No context, no transition, no meaning in regards to the rest of the course. This upsets me, but, I've got nothin'. Any ideas?
I feel that this is a new and exciting way to teach algebra 1 that could produce some amazing results. I'm a little nervous about showing this to those who are teaching alg. 1 next year because its so different than the way it used to be, and also because I'm not teaching it (so that will produce some interesting discussions as well).

Snow, man.

Checked out my 101qs submissions today to see the low perplexity scores. After checking up on Dan Meyer's blog I realized that my 'Snow, Man' pic had an honorable mention in his Top 5 for this week. I won't lie, I got excited. However, after reading his response to it, I realized that I had missed the mark slightly. My picture gives way to some basic questions, but could be better if planned out.

I would imagine if I showed this picture to my students I'd get questions like, "How much snow is that? What is the ratio between the three balls? How long until it melts?" and so on. These aren't bad, but are they really any better than a textbook problem? After all, the whole point of Act 1 is to get the students engaged and really interacting with the math behind the situation. I need something that will stimulate independent thought and make the students care; something that will allow them to envision themselves in it. Everyone builds snowmen, but who really cares about how much snow they've used to build it?

After reading the comments about how to redesign the problem, I've got some ideas to reproduce this in a few months. I liked the idea of comparing it to another snowman in a neighboring yard - introduce the competition element (after all, everything's better when there is a winner and loser). I could start by showing an aerial view of my yard along with a time-lapse video of me building the snowman in a methodical way, clearly using a certain amount of my yard. I could then pan out showing my yard again with the amount of snow that's been used already and the amount left. 

This could still produce the same questions as before, but now it could be expanded to "Who's snowman is bigger? What is the biggest possible snowman that could be built? How long would it take to build such a snowman? Could you combine the two to make a super snowman?' While these questions may not seen anymore advanced or intense, the redesign could get my students involved more. It wouldn't have as much of a 'ugghh, not this again' context, but would be more inviting. It would be more practical, more relevant, more realistic to their lives. Getting them engaged and thinking is the key, and this might just do it. I'll let you know in 9 months.

This has made me realize that I still have some work to do in creating these First Acts. While it can be done with almost any picture or video that inspires thought, they key is using the best possible option and format. Taking a basic picture like that above works, but does it work as well as I think? I need to think about these from a students' perspective and a teacher's perspective to get the best possible Act. Practice, practice, practice. Thank you 101qs and Mr. Meyer!

Piece of Cake Upside Down

I recently re-watched one of the few good math movies made - 'Stand and Deliver.' I showed it to my students and they were (surprisingly) interested in it and loved it. Some of them learned shortcuts to their 9 times tables and a new way to think about positive and negative numbers. I, on the other hand, watched it from a new point of view.

I haven't watched this movie since I've become a teacher. Previously, I watched it from a student's perspective and purely for entertainment value. Now, as a teacher, I realize there is some deeper content here. There are some things wrong with the clip above. The claim that their students cannot learn because of where they live or because of their status is bogus. Mr. Escalante gets it right when he says 'students will rise to meet your expectations.' I think there are a good amount of teachers out there that don't fully believe this; they think kids will be kids and there's nothing that can be done to help them. They are who they are and there are all kinds of excuses for the teachers not to teach them. Escalante owns up to his responsibility, says he could do more, and he follows through with it. After watching this again, I began thinking about my classroom. Do I set a high level of expectation for my students, and continue that expectation throughout the semester, or do I eventually cater to their level? Can I get them to do more for me and for themselves in order to help them realize their true potential? Is there a way for me to give them the ganas they need to be successful not only in my class, but in their lives? If I answer in the negative to any of these questions, what can I do to change? I plan on seriously reconsidering my first week of class and my management techniques to empower my students with ganas. Yes, I teach math. Yes, its an uphill battle before they even walk in the door on the first day because of that. Yes, stereotypes say that I am a boring nerd. I don't think that I can settle for any of that and I don't want my students to either. I need to find a way to change their opinions, change their mindset, and change their opinion of their ability level. I need to gain their trust from day one and show them that they are capable of whatever they put their mind to. I feel I do this to a point with some students, but not as many as I'd like. I also realize that this is a Hollywood interpretation to a true story, but there is a lot to be said for it. I could go on and on...

12 Inches of Math (informer!)

We built our first snowman with our daughter this weekend, and it was a tremendous amount of fun. She didn't do much work, but she gets excited everytime she sees it.

I've been trying to harness my inner-nerd this year; trying to find math in everything I see and do. I figure if I want my students to see math in the world, I need to be able to see it too. I imagine this is how Mystery Guitar Man approaches his videos: searching for music in his everyday surroundings and discovering how he can use those sounds to create something new and original that is both visually and audibly pleasing in order to send the message that music is everywhere (hence my previous post, worlds collide). I feel that I'm getting better at recognizing various situations and their mathematical values, but it's taking some time to develop this mindset.

After building our snowman, I realized that there really wasn't that much snow on the ground to begin with, which you can tell from the dirt and mud in the picture, it was just the perfect wet snow for building. I wondered, how much snow did we use in building that snow man? If we would've used all of the snow in our backyard, how big would our snowman be and would that beat the world record? How much snow actually fell (not just how many inches deep)?

I realize that if I'm following the mathematical storytelling model, you should come up with these questions, but they were just some thoughts. Essential info will be posted later (before the snow melts).

Anything wrong with this?

Just watched a lecture from Will Richardson at Millersville University on technology's impact on today's education and had to post something. 
The one part of the lecture that caught my ear was the idea of letting students use the internet during tests. I, for one, am on board with that! I'm not anti-teachers (obviously) or anti-education in any way. I agree with what he said about the way the world is changing is causing education to change with it. He made a great point when he asked the crowd who was going to buy an encyclopedia this year. When I was in school, that was the #1 source to find information. When I had to write a paper, I read through an encyclopedia first and then found other books in the library. In college, the first thing I did was look online. Times have changed, so lets change with them.
One thing that came to mind was a video that Dr. Heitmann actually showed me (and it still might be on his website) called the 15-minute university. Its a comedy routine explaining what the average graduate remembers 5 years after they graduate (in math, its the Pythagorean Theorem, which is true). Most students don't remember 95% of what they learned in their 12 years of schooling 3 months after they graduate. If they need it, they're going to look it up. Why should we make students memorize formulas or properties when they are literally seconds away.
Again, I reiterate that I'm not saying we shouldn't teach anymore. I believe we should continue to teach our curriculii (??) and make it meaningful to our students. But there really is no point to making them memorize everything (because if they're interested, they'll remember it anyway). I've taught proofs in geometry for the past five years and I used to make my students remember all 70 of the theorems we learned thoughout the course. I later decided to make them remember just the important ones. Now I make them remember none of them. They are allowed to use a list of theorems during proof tests because its a waste of their time to memorize them. During lessons and through homework, it works out that they end up learning the important ones anyway, so it all works out in the end. They are not missing out on anything and they are not leaving my classroom without knowing that vertical angles are congruent or without knowing the transitive property. They have a full understanding of these topics, I just don't require them to sit down and stress out about them. I help them gain the appropriate knowledge through my coursework.
The question that comes to my mind is: how can I allow my students to use their notes/internet/whatever they want during tests, but still make sure they are able to pass the keystone/pssa exam? Unfortunately (as much as I hate to use this as a reason) these tests are the only thing that justifies not allowing students to do research during tests and projects. I hate using state exams as a reason for doing anything in my classroom, but it is what it is.
Feel free to disagree/agree with me

Students in the Real World

I've had the luxury of teaching the same courses for the past five years. I'm the only teacher in the building who has taught one of them throughout that time, which means I've been able to adjust the curriculum to meet the needs of the individual students from year to year. Today, I thought of an idea that may make the course much more interesting for my current crowd: I think I'm going to let them create their own math problems.
Now, they're not going to create meaningless problems, with random numbers and variables that have no context. I want them to live their normal lives, but when they see or hear something that captures their interest I want them to turn it into a problem. Their job will be to take pictures, videos, recordings, etc. of something the interact with and come of with a question that they (or someone else) can solve. They will have to be able to describe the scenario in words and visually, come up with a question or multiple questions, and also gather the information that would be needed to come up with an answer. I don't care what math topics they choose; it could be any high school level math. If it involved something they haven't learned, then we'll go through it as a class. If it uses information they already have, then they'll come up with an answer. Either way, its math in the real world.
Since I've started my career as a math educator this is something that I've spent a lot of time thinking about. Every student always wants to know why the topics they are learning are relevant. They don't settle for an answer of, "You're learning it because its on the test," anymore. They want substance and meaning. If I want my students to see math in the world (which everyone should want this), why not let them explore it themselves? I think if I organize this project correctly, some of their eyes might be opened to how much math is used.
I'm at the point where I see situations or objects and my mind jumps to 'How did they do that?' or 'What if it looked like this...' I want my students to become that way too. This will lead to them being life-long learners and it will exercise the creativity of their minds. If I can get them to analyze any situation and expand upon it or just wonder about it in a new way, I think I've achieved something.
Let's hope this goes well!

iAwesome

So I just found out about Apple's iBooks Author app, and got extremely excited. The idea that I could create my own textbook fascinated me. I could be sure that my students received the information they needed and it corresponded perfectly with the way it was being taught. No information would be switched around, there wouldn't be any jumping around, and I wouldn't have to worry about teaching topics that aren't in the book. Even if I just made a textbook for my classroom, there could be tremendous benefits. By making 'personalized' text books we could cater to the needs of our students, our district, and our teaching styles. To me, this is much better than an online course (even though they are closely related) because the material can be written in the way that works for the course and the instructor. Earlier in education, curriculums were driven by textbooks. Teachers would follow a book from chapter 1 to chapter 20, one after another, and use all of the resources that came with that book. Now, with all of the common core and assessment anchors and standardized testing and everything else that's (invalid) and driving education, teachers are creating their own curriculums and moving all over the place in textbooks. If we need to create our own courses, it only makes sense to create our own books that follow that course.
Now, I'm not 100% sold on the idea of an e-textbook (and my school does not have classroom sets of iPads), but still, just the thought of it is awesome. It would be something that I would love to try.
My only quarrel: the software only runs on a mac, which I do not have. I need a PC version so I can create a textbook (or $$$ so I can buy a mac and iPad).

Give 'Em What They Want! (part deux)

After school today, I was telling a former student of mine about a final project I'm putting together for my geometry class. Another teacher and I are creating a project where the students will be broken into 'companies' where they each take a job. Together they must work together to create the school of the future. They will need to create an architectural drawing of the building and the surrounding area, construct an actual scale model of a classroom, calculate the cost of construction, and put together a formal presentation that they will give to school administrators (among other things). Talk about authentic!?!? Anyway, my former student thought this was a great idea and immediately saw the value in it. He actually told me he wished he could've done this when he had me two years prior.
This got me thinking, why don't I give the students what they want? Throughout my educational training and research, I've heard a lot about how students desire to see where their education will pay off. They want to know how their knowledge can be used to benefit their lives. This project we're creating is huge and will take a tremendous amount of work for the students to complete. Its intimidating. However, in the end (or while their working on it) I know my students will see value in it. It takes the big ideas from the course and applies them to a practical, real-life scenario.
Will all of my students become architects? No, of course not. They know that as well as I do. However, this project shows them one way that they can use their geometry knowledge and they'll be able to translate it to other situations. And plus, its something different. They've taken enough meaningless tests; they want to show me they've learned everything through a different medium.
I have a few other units where I have my students do projects instead of taking tests. My goal is to eventually replace all of my exams with projects, but I'll take it one step at a time. If they want it, who am I to deny them?

Sometimes I Forget

(I know, two posts in one day. Clearly I'm excited about this)
In my geometry class we're currently studying circles and all of their glory. We've focussed mainly on arc and angle measures formed by secants, tangents, and chords, but I decided to switch it up today. Because of the shortened block I gave them a quick lesson that involved circles and Pythagorean Theorem (world's collide). I didn't reteach the Pythagorean Theoem, I didn't review all of our work with circles thus far, and I didn't dive into a big speech about how math is relevant to the real world. I took a page out of Mr. Meyer's 3 Acts just to see what would happen. The result was spectacular.
I drew a cirlce on the board, labeled it 'Earth,' and then drew a tiny mountain on top. "How far can you see if you stand on top of this mountain?" My students proceeded to tell me what information they would need; I told them how tall the mountain was, someone shouted out the radius of the Earth (which surprised me), and they wanted to know what angle they were looking at. I went through the problem, showing how their field of vision forms a tangent line with the Earth (horizon) and they quickely figured out how to calculate this distance.
It was amazing to watch their expressions as we went through this problem. They were more focused during this 15 minute lesson (on a topic they already knew I might add) than they were on anything else in this unit. Sometimes when I'm caught up in the 'I've got to cover all of this' mindset, I forget that students LOVE when the material makes sense to them. I never saw this type of problem until I started teaching, but if I would've seen it as a student the Pythagorean Theorem would've made much more sense, and I would've cared more. My students figured these problems out in a heartbeat and there was no questions of 'When am I ever going to use this?' Granted, they might be on an airplane and wonder how far they can see, but most of them will not get out their calculators and actually figure it out. But they thought it was awesome just knowing that they could if they wanted to.
I need to remember this as a I teach more often. Students crave this kind of thing. If they can see it and use it, they don't care what subject or topic it is. Once they're hooked, they want more. Many of my classroom issues could've been alleviated had I thought about this during previous lessons. My hunt is now to fill in these gaps in my lessons to provide my students with the situations they want. Why would I not give them what they want?