Inspired by Coffee

The other day I was sitting in a coffee shop and thought to myself, "Self, this is a nice place to be. I like sitting here." To which I responded, "Yeah, why don't our classrooms look more like this?"

Not the actual shop, but you get the point...

Internal monologues aside, I have honestly begun to wonder why we don't draw more inspiration from places that people enjoy spending time in? What if our students actually enjoyed being in a classroom? Next year, for the first time in 7 years, I will have my own classroom... I desperately want to make it a space that feels good. I might even spring for an espresso machine. 

Today in 9th Grade Math

There is something to be said for the gamification of education. I couldn't believe how motivated my students were to win little plastic rectangles.

Today we started playing Blackjack!

I had no real curriculum with my 9th graders so I've used the year to explore ideas... I've had some great successes and some lackluster results. Last year the previous 9th grade teacher had taught some probability so I figured I'd follow his footsteps, but I wanted to do it by playing games not by marching page by page through a textbook.

Today, we started playing blackjack. I'm not 100% sure where we are going math-wise, but I know there is more math in Blackjack than my students (or I) can handle. There is a lot of great thinking in developing a strategy and plenty students can learn through simulations and gathering experimental data. I can't wait to see where this goes!

Death by Definition?

In the world of standards and the increasing need to document and define, what does Robert Pirsig's thoughts on Quality mean for us as teachers and for our students?

"Quality cannot be defined. If we do define it we are defining something less than Quality itself." – Wikipedia

I can't get this quote/statment out of my head. Wondering if we are better off to lead by example than by definition or standard. Isn't that the danger of math that we boil everything down to well-defined rules and turn our classes into exercises in completing algorithms?

Introducing Radians

I usually introduce Radians via the unit circle making an theatrical argument that degrees come from Babylonian religious views regarding numbers with lots of factors and their base-60 number system (all true or at least plausible as far as I know). This begins to make the argument that maybe a better system could be devised, one based on logic and geometry, but this approach has always fallen short of allowing the students to make the jump to radians.

So last year I began to experiment with sectors to build up arguments that arc-length and radius determine the angle. I saw some success, but I had left it too unstructured for the students to reach a meaningful conclusion. When I tried to make a jump to radians I got a lots of looks that said, "I got what we just did, but what does THIS have to do with THAT?"

This year I gave the sector thing another shot, but this time narrowing what I asked them to look at. I defined arc-length and a sector and got them working on tasks like:

At this point I asked them to create an equation relating arc-length, radius and the angle. A few arguments broke out (Awesome!), a few questions were asked and virtually all of the students wrote down something akin to:

From this I asked the question "if you know the arc-length and the radius can you tell me the angle?"  I had the students draw a sector whose arc-length and radius ratio was 2 and then measure the angle... Each student had a different sized sector but all had the same angle. This lead to a conversation about ratios where a student pointed out that: 

Awesome! 

With a little math teacher magic, and no mention of radians, by the end of the 65-minute period I had most of the students agreeing that:

The next class we talked about the "arc-length" of a full circle. We worked our way around the unit circle talking about half and quarter circles before jumping into smaller angles and coming up with radian equivalents for the typical 30-45-60 angles. Only at the end did I finally mention the name "radian." 

I've followed this up with a few "Pop Quizzes" that were not graded, but just a bit of practice estimating and sketching angles in radians. Quiz 1 and Quiz 2. 

The result is the least confused class I've ever had. Dealing with radians still takes some effort, but they seem to get it.

My handout with the sectors can be found here via Google Docs. The rest of my trig bits (a work in progress - isn't everything?) are in a Google Doc/Drive collection. 

Can You Guess When The IB Exam Was?

A few years back I posted my physics class notes on a wiki after an email request to keep the notes publicly available. As all good nerds do I watched the traffic with Google Analytics. I'm not here to brag, my site has seen less traffic in 4 years then a successful commercial site sees in a week, but I noticed something interesting the first May that the site was up and running... There was a huge spike in traffic for 1 or 2 days. The same happened the next year. Can you guess when the IB Physics exams are?

If we think our students aren't cramming, we're wrong.

Update: David posted the image to Dan Meyer's 101qs.com. Man, was I wrong, it generated all kinds of questions...

What Got Me Thinking - May 18

Student's Brain Flatlines in Class - Differences in brain activity between class and labs is amazing. One more argument that what we are (often) doing is not engaging our students.

Estimating Gravitational Field Strength

Saw this on Dan Meyer's 101qs.com this evening. What a great photo to clearly show the gravitational field strength on Earth.  I don't like the term "acceleration due to gravity" as its wrong or at best misleading and incomplete, but that's the subject of another post.

This could make a homework assignment and or a great introduction to Logger Pro's video and photo analysis. Plenty to talk about in terms of estimation (of lengths), center of mass, horizontal velocity, etc.

BTW TinEye Reverse Image Search is a great way to find similar photos or in the case above same photo but different resolution. 

Free Dropbox Space - Am I Cheap or What?

I hate monthly bills, I just despise them. So the thought of paying a monthly fee to store my files with Dropbox frustrated me - no matter how much I appreciate the service. IB students are required to do written work - even in math. They turn their work in via Moodle and I return it via Dropbox in a shared folder. This had two results:

1. They will now have an digital portfolio of all their work.  
2. I got free space! 

So far 2/3's of the students have completed the necessary steps for me to get extra space! Not too shabby and cheaper than the Lifehacker solution.

If you haven't tried Dropbox and want to here's a link (wink wink) Dropbox.

What Got Me Thinking - May 9th

TEDX - Gaming for Understanding: Not the usual take on learning through gaming.

Mathematics Education for a New Era: Video Games as a Medium for Learning - I am enjoying the arguments regarding the validity of games (and gamers) the book it continues to shed light on why and how games can and should connect to education.

Toilet Breaks Land Speed Record - At least BBC doesn't make this headline news like CNN might...

Google Apps is Everywhere - US DoD is adopting Google Apps for 90,000 employees. If the US government can do something then any school should be capable too. -- My school is in the process of adopting Google.

Changing Assessment - Talking points from David Martin (along with his Prezi). Good Stuff.

3D Vector Magnitude

After watching my current IB year 2 students struggle with vectors (I took over the class this year) and it was the 1's turn to push slog death march through vectors I was determined to slow down and make sure they understood the basics... Or at least give them as much time as possible to create some conceptual understanding (certainly not the same thing).

We started vectors by talking about different notations and their meanings. We talked about the magnitude of a 2D vector. They could see the clear connection with Pythagorean Theorem, a few even suggested its use, but the 3D formula was not clear to them. Not at all. Students suggested we could use a cube root or cube the coordinates. Both potentially valid extensions of the pattern for sure. I ended class by giving them the formula with no proof no justification - time was running out and I had problems I wanted them to finish. Oops.

Realizing the obvious error of my ways, I started the next class with a model of a 3D vector (I used a wire coat-hanger as the vector and large graph paper to form the X-Y plane). My model was just to show them what I wanted them to build. Their task was to use a meter stick as their vector - which required some engineering - and find the coordinates of the vector in 3D. A few students suggested aligning the vector with a coordinate axis... I nixed that idea.

Once they had the coordinates I asked them to prove the formula given in the last class or better yet  to ignore the formula and use only the coordinates to find the length of the vector - which they already knew from the meter stick. 10-15 minutes later folks had drawn right triangles and created a solution!

Once everyone was finished, I pulled the whole class over to one of the more neatly created models so I could point and formalize the ideas.Towards the end several students commented "oh that makes sense," or "now I get it - that formula does make sense." Voila! A simple but effective way to spend 40 minutes of class.

How to Teach Math Anxiety

Maybe this one has been bumping around the interwebs for awhile... Today was my first encounter with it thanks to David Wees. Too good not to share.