Sunday, January 29, 2012

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!

Sunday, January 22, 2012

P(calculating the odds)

So, I was listening to the radio tonight and heard this story and I thought to myself, "Wow, what are the odds?"

But seriously... what are the odds?

Friday, January 20, 2012


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).

Tuesday, January 17, 2012

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?

Thursday, January 5, 2012

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?

Natural Geometry

Mathematically beautiful. I woke up one rainy morning a few months ago and saw this on a bush next to my back porch. It caught my eye for obvious reasons. So many questions came to mind. I've seen spider webs before, and while they're fascinating to look at and to think about, this one was different. I've never seen one in a nearly-perfect parabola/cone shape before. Its times like this that I wish I would've stopped to take some measurements or had all of my students standing next to me. This could've been (well, I guess it still could be) a great exploration of paraboloas and calculus. I'm just glad I stopped to take a picture. When I got home it was no more.
And how the heck does it appear to be levitating?