Curiosity?

Now I'm curious. I wonder what this would like. Would you be able to predict the number of letters in any number (even though it would be easy to count)? What kind of relationship exists? I smell a project....

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).

We Built This City



How tall is he? And how much does he weigh? How much does he have to eat in order to live a healthy lifestyle? How does he rock so hard?

Betelgeuse, Betelgeuse, Betelgeuse!!

I was talking with one of my colleagues about how we can improve problem solving skills within our students to encourage higher-order thinking skills. In the past, I've shared with him Dan Meyer's 3 Acts and he was as amazed as I was. Together, we've been working on creating problems for algebra1, 2, and geometry that are set up for this process, and he shared with me a video similar to this one that he showed his students. It's a simple video; there's nothing fancy about the way its made and there is no narration, but the possibilities are endless in the way its interpreted. He used it to illustrate scientific notation. My first thought was to ask the question, 'How many Earth's fit inside Betelguese? How many suns fit inside VY Canis Majoris?' You could relate it to similarity, 3-dimensional space, fractions, or a hundred other topics. Regardless of how I end up using it, I plan on removing the diameters from the video so that my students can do some research to find the information that they think they need to answer their questions.
This video further illustrates to me how many questions can be generated from any picture or video. The phrase 'a picture is worth a thousand words' has become more real. I now try to look at my everyday surroundings from a mathematical perspective. I always tell my students that if math didn't exist, nothing else would either, but they always blow me off. Now I'm beginning to gather solid, concrete examples that they can see. I think the way I'm going to approach it from now on is show my students these examples so we can explore them as a class, and then use them to illustrate that math truly is everywhere. If I can get them to believe this, them I'm one step closer to getting them to appreciate everything that happens around them at any given moment.

So, what are your thoughts? What questions come to mind when you see this video?

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!

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?