Tracking - Shades of Not-So-Awesome

I have arrived at a new school that has an old structure in the math department. We track our math students both by age and supposedly by "ability," starting in 8th grade. There are two levels of math for each age group, the "normal" and the "advanced," yet 90% of the student body are in the supposed advanced class. Added to this pedagogical flashback is the fact that we offer scholarships to high achieving local kids (we're private). We pull some of these kids out of fancy math and science schools only to put them in "9th grade math." We match them with like-aged students not in a class that might challenge these gifted and motivated kids. The result is many shades of not-so-awesome.

While slow to start the wheels of change are beginning to turn. The conversation of how our math program should be shaped is beginning...

So how would you do it? If you could have your choice of how to organize math classes grades 6 and up, how would you do it?

Why Math?

I found this talk brilliant. Let's be honest with our kids. When will they use what we are teaching them? And why are we teaching them the topics that we are teaching? I'll let the video speak for itself.

Amen.

Logically vs. Mathematically

Today in class I overheard, "I tried it logically at first and then I tried it mathematically." It made me laugh a little, cry a little, and I had to force back the teachery knee jerk reaction, "But math is logical!"

The statement says so much about how our students view math and math class. If math isn't logical then we are doing something wrong, but I guess we already knew that.

While the statement made me sad, was this a case of actions speaking louder than words? The students were doing exactly what they should be doing, talking and working out how to solve a problem. Can a teacher ask for more?

Why Smart Boards?

I desperately want to embrace and make use of the smart board in my classrooms, but only if they make my classroom more student-centered or allow me to do things I can't already do given a computer and a projector.

While smart boards are undeniably wonderful eye candy and there are some good uses for them I have recently begun to question the value of the smart board. A quick google image search almost universally shows one person using the smart board and many others watching them... Ugh. That's not what I want my classroom to look like.

Is this photo doctored?
Check out the teachers shadow...

Have smart boards simply become something that teachers expect to have? Are smart boards really changing the way we teach? Are smart boards allowing students to learn more or in different ways? How does a smart board allow a teacher to create a more student-centered classroom? How does a smartboard beat a tablet and projector?

I am not an anti-tech guy, far from it, but I don't want technology for the sake of technology. I want technology that improves on what I can already do or even better lets my students answer questions they couldn't previously answer...

What are you doing in your classroom with a smart board?

Looking for Feedback - Radical Roots

I'm looking for a bit of feedback on an investigation. I am teaching an algebra heavy geometry course, we just tackled right angle trig. The kids have seen Pythagorean theorem and such... I need to teach radicals and exponents at some point and this seemed like a reasonable time with areas of polygons and coordinate geometry around the corner.

The objectives of the investigation is for students to:

• Develop geometrical meaning of square roots 
• Develop geometrical meaning for equivalent radical expressions such as:

I must admit most of what is posted is not my idea, but an adaptation of content from Math Alive! Course III.

Link to the Google doc investigation.

Any and all feedback is welcome.

Your math teacher might be a sleep deprived idiot...

This made me laugh. Yes, I am the teacher who wrote this question... Probably a clear indication that I need more sleep.

I loved the honest feedback from the student.

I love it when a plan comes together!

I was working my way through right angle trig. It was going pretty alright, but I was looking for an exit strategy that would tie in RAT to the new topic... Polygons, Surds, Exponentials. I saw connections to all of them and I was flip flopping between topics unable to choose. Seventeen ideas running through my head... Where's my Ritalin?

Then Kate Nowack of f(t) fame tweeted a link to a video:

There is genius in this video. Maybe not original math genius, but genius all the same. The connection was obvious. Pythagorean theorem and maybe some trig. Best of all students would need to think about lines, angles and triangles. Perfect.

I didn't really like the way the question was framed, felt like he gave away a bit too much (even in the original video, the one above presents the solution), but it does make for a good video. Before class I drew a series of 4 dots on all of the whiteboards, providing spaces for the students to present their results with some semblance of order. Each time an improved result was written up the class was drawn to it and they madly checked each other's math.

I heard things like, "that side is a hypotenuse and the other side is 1, so that side (the hypotenuse) is more than 1!" Or, "you used 0.333 instead of 1 over 3 that's why it didn't work!" Freaking awesome.

30 minutes in, I stopped class and asked how many wanted more time? Almost unanimously they wanted more time. I gave them the option of seeing the answer, but they didn't want it. What more can a teacher ask for? Finally, I ended the 65 minute period with the video and a brief discussion. During which one student asked, "Do mathematicians really play with soap bubbles?" With a twinkle in my eye, I replied, "Yep."

Math is real. Soap bubbles are real. The learning was real. No pseudo-context needed.

So close...

I am teaching Geometry for the first time this year. Which means I get to teach right angle trig from scratch! In the past I have taught trig (circular) functions, but never the more basic bits.

I was supposed to teach "triangles" which they already knew and had for some time (my school seems to have accepted that math will be boring and repetitive). So rather than belabor the point, I did a quick review of terms that led to the idea of similarity. I had them apply the idea of similarity to bigger things, like the school building... or the playground equipment... or the local mountain top.

Within a class period most if not all understood the idea that the ratio of two sides of a triangle can only be changed if the angle changes, in fact when I brought it up half the class gave me that look of "duh mister, we figured that out." This was all done with no mention of sine or cosine.

With the real learning done, I started into a bit of formalization. With a short back and forth discussion that required students to draw a few more triangles to convince themselves of a the details we had the 3 main trig functions on the board in just a few minutes, but still unlabeled.

With nothing more to teach I finally labeled the functions...  I gave them some typical problems to practice with, only one of which I did on the board. Then they were off and running. I felt so close to a masterful introduction of trig. So very close.

Next on my list was inverse trig functions...

I posed the question (with a drawing on the board), given two sides of a right triangle how do we find the angle? I figured there would be lots of drawing and struggle to draw the correct triangle in order to measure the angle. So close, I could almost taste it. Somewhere somehow during this time someone shared that they could use the calculator to find the angle, i.e. inverse trig functions. They don't understand inverse functions, but they have buttons to push...

I was so close. Sometimes I despise the power that buttons seem to have over students.

Should I have given them a table of trig functions instead of allowing them to use their calculators? That seems so contrived, so fake, so false. How do I avoid this next year?

Transformations Take 2

This year my usual transformation of function investigation didn't seem to work. I suspect it was not the investigation itself, but rather my students adjusting to a new classroom culture, one where the teacher doesn't tell you everything...

We took a break from functions and function notations to work on an investigation with some toy cars (post of that may be coming if the results are half decent), but I promised the students that we would revisit the topic of transformations. Its simply too core of a topic to move on with half the students not grasping the idea.

Searching for a new way to tackle transformations, I found one it was brilliant! Then I forgot the idea and came up with this:

http://www.geogebratube.org/material/show/id/708

Using Geogebra I created a simple transformation applet (link just below the pic) allowing them to graph any function and adjust the 4 parameters, do reflections, plus the nasty bits of absolute values. Paired up with the applet was a worksheet to guide them through.

The results seem to be far more positive and constructive. They seem to understand that they will need to ask questions and do their best to organize the answers and their understanding. I will of course do a debrief afterwards and to try and scoop up one or two lost students, but "take 2" seems to be working

Throwing Stones...

The day after getting totally riled up by Sal Khan  I feel frustrated with myself. I find that what I am doing in my IB classes looks more and more like lecturing. Why is this happening?

A little background: For my own organization I write up notes and post them on a website, I began doing this years ago in physics and got more intent on publishing my notes at the request of another teacher. A request that came in via email...

The other day I assigned some reading from my site. I did this simply because I couldn't figure out how to convene the information in a student-centered way. Judging from their understanding it seemed to work or at least no worse than if I had lectured. Judging from Google Analytics they spent about 13 minutes reading, which is considerably less time than if I'd tried to lecture.

I can make excuses; I am teaching 4 new classes at a new school in a new country, I can't seem to get a grasp on what my students understand or the class dynamics of having 5 students makes discussions almost impossible. This last excuse bothers me the most as it is a result of my school's desire to "track" students in math. But in the end my IB classrooms are not the dynamic interactive classrooms that I used to have or want to have.

On the flip-side. If having my students read was (relatively) successful does that mean that reading is a good option? If I can't, for whatever reason, find a better way to expose students to material than to lecture is reading then good teaching practice? 

So if I start to use this tool more and more then how different am I from Sal Khan? 

Sometimes I feel like I'm throwing stones in my own glass house. 

Sal Khan did not Invent the Personal Classroom

As he so often does, Dan Meyer got me curious with his latest post on Sal Khan. I wanted to see and hear Sal Khan for myself (again). Several quotes were troubling, one of them was regarding schools and teachers who have been using Khan Academy videos:

They [Teachers] took a fundamentally dehumanizing experience - 30 kids with their fingers on their lips, not allowed to interact with each other. A teacher, no matter how good, has to give this one size fits all lecture to 30 students - blank faces, slightly antagonistic - and now its a human experience. Now they are actually interacting with each other.

Taken from Sal Khan's TED Talk  (starting at roughly  7:00).

I take major issue with the implication that no matter how good a teacher is he or she must lecture to their students. Being good has nothing to do with it. Its a matter of philosophy and approach. Its a matter of implementing best practice, which should involve as little lecturing as possible. Lectures are dehumanizing when the target audience is 30. How much more so is a video that is targeted at thousands or millions? Where is the ability to adapt to student needs? Where is the ability for students to ask questions?

The Khan Academy might be an improvement over teachers who don't teach (they lecture), but lets not pretend that a 20 minute video has created a sense of humanity in the classroom. Lets not pretend that videos watched at home allow students to talk and work together in class. It is the teacher who must realize that their time spent with students is best spent actually talking with and listening to students not talking at students from the front of the room.

I am not of the opinion that Sal Khan has it all wrong, but I think his perspective is skewed. He sounds a bit like Al Gore claiming he invented the internet. Sal Khan did not invent or allow the creation of a personal classroom he created a set of (boring) videos.

Mutual Humanity in a Classroom

A week or two back, I made a few large mistakes when I was beyond tired. (A new school and new country will do that to you.) They weren't mistakes that I could easily recover from as they were in print and I was struggling to function let alone think clearly enough to wright the ship mid-class. My students were shocked that I admitted to a mistake! 20 minutes later I heard them talking in the halls that the other math teachers never admitted to mistakes...

Last time I checked students and teachers, even math teachers, are all human. To ignore our mutual humanity (I  have yet to fully understand what that means to me) and pretend somehow that I as a teacher am superior or significantly different is to lie to our students and will likely make our jobs in the classroom even harder.

Homework as Review?

This year I am exploring the idea of using true homework solely as a review tool. I feel strongly that typical homework is rarely useful and 80% of the time (or more) it falls into one of two major categories:

• Student's know how to do it, so its boring, emphasizing that math is boring and repetitive. 
• Or student's don't know how to do it, so they spend hours being frustrated, emphasizing that "they are not good at math" or that "math doesn't make sense." And often the next class period is spent "explaining" the homework.

Yet I do see the benefit of students "practicing" and working through problems on their own.

So what if homework was just a review tool? What if students were given a week (or more) to grasp material and work through their questions in class? What if homework was assigned only on content that is not currently being covered in class? 

To me this looks something like this:

Where each color represents a different topic or sub-topic. Week 1 in class is spent working of Topic A. Then Week 2's homework focuses on Topic A. Finally, during Week 3 there is some sort of quiz or assessment on the topic. 

Things I like about this:

• Students are forced to work with a concept for a longer period of time, without giving up more class time.
• Students are given time to struggle and learn with the support of their classmates and the teacher rather than trying to learn at home by themselves.

Things I don't like:

• It doesn't begin to deal with the "boredom" factor. It might even emphasize it more...

The Moment

The moment students realize they can't just memorize their way through math class is a special moment. The moment students know that they need to "understand' not just remember is one of my favorite moments as a teacher. Today that moment occurred!

My IB Math kids just saw IB questions for the first time... They were almost annoyed that they needed to go look through past notes. Seeing problems that didn't scaffold the 3 steps to get to the answer. Seeing that they will need to THINK!

Awesome.

What do you do when...?

What do you do when 4-5 students in a precalculus course are asking what a cubic or even worse a quadratic equation is? Me? My jaw dropped. I was nearly speechless. My response was on the verge of disrespect/disbelief I simply couldn't wrap my head around the idea.

How in the world have they made it this far in math and they can't identify a cubic, quadratic or exponential equation?

For a good while I felt like the most awful teacher. Here I had them looking at limits and how fast functions approach infinity and they don't know the difference between a quadratic and a cubic function. Then I thought, wait I didn't teach them those functions... I can blame the other guy. With the finger pointing done, I thought about how cool it was they were understanding complex ideas like limits!

Adding to that list I think this is, to some extent, an indication of the state of math education. I care about vocabulary only so far as it allows my students and I to have a conversation using words not just symbols. My students know how to deal with quadratics on paper they just don't know what they're called.

I have never done "matching" on a test. I think my next quiz will have a vocab matching section...

Follow Up: Sequence Intro

Oh how a trip to Target can lead to good things in the classroom!

I came up with a few ideas for many students to play with to get them started playing with sequences. A little tactile learning if you will... They even went a bit into the idea of series with out them really knowing (or caring).

I had them try to make a stack of ping pong balls 4 layers high with the least number of ping pong balls. (I was very careful in the write up to always say "ping pong balls" not just "balls." Just a bit of classroom management.) This of course led them all to the same solution of creating a triangular pyramid. They looked at the number of ping pong balls in each layer and how the number in each layer increased. I really like the idea of setting a challenge that would lead them to a solution, sure wish I could have figured out more of those!

Stacked ping-pong balls

I also had them look at "stacking circles" (i.e. poker chips). They placed one chip and then surrounded it with rings of different colored chips (just for visual separation between layers).

Poker Chips in rings

Both of the ping pong balls and poker chips were fun and tactile, but the patterns were a little difficult for them to describe in a more formal way (read:  with an equation). The poker chips were difficult if you include the original chip... So ala Jo Boaler (a book well worth reading) I had them move on to geometric patterns using foam squares, made from foam sheets I picked up at Target in the craft and scrap booking section.

With the foam squares they could get a little more analytical, as the patterns followed function forms they were familiar with (linear, quadratic and exponential). They made tables of numbers, graphed the results and final were able to create equations to describe the patterns.
Reflection on the process: A few students really enjoyed the change to a bit of tactile learning, something I really need to remember. The process of making connections from squares to table to graph to equation (i.e. from concrete to abstract) was, I think, highly valuable. That process is at least closer to "real math" or "real science." It also served to slow down some of the folk who like to jump straight to the equation, thinking equations are what math is all about.

The handout I gave the students is a google doc.

Exploring patterns

Back from spring break, time to get chugging...

I am getting close to starting sequences and series with my kids, probably do that by the end of the week. I have my usual inquiry style group work put together from last year, but its pretty boring. Not as boring as me standing up in front of the kids for 2 periods, but not awesome. I want to find something more interesting to start with, then I'll go back to what I did (successfully) last year.

I've been searching the inter-webs for ideas. Patterns the kids can build or observe on the desk in front of them. I see the usual suspects of the sea shells and Fibonacci...

The curve doesn't fit... How am I suppose to convince students it does? And why would I?

Textbooks suggest the always exciting interest rate based problems. I can already see the eye lids drooping and the drool starting to flow. The books also had some brick stacking problems (which might work) or the oh-so inspiring stadium seating problems...

I'm looking for something that can be posed as a challenge to create something that's not 100% obvious. I want the kids to create something, have I said that yet? So far my candidates are:

1. Sphere stacking - Stack x number of spheres to create the tallest structure.
2. Packing circles (creative I know) - start with one penny, completely surround it, surround those...
3. Dilution of liquid - dy/dan style I love the potential to explore the idea of limits
4. Mowing lawn or harvesting hay in increasing or decreasing circles 
5. Stacking blocks - Stack x number of blocks on top of a single block to create the shortest possible structure 
6. Creating a spiral out of square blocks 

I want 3-5 good ones. So the students can explore multiple different patterns. There also needs to be a level of engagement, something my textbooks simply don't have.

I may also explore going in different directions. Such as giving an equation and asking them to create a visual representation of the pattern. This could be done with linear, quadratic equations even exponential...

Another option would be for me to create a pattern on paper, have the students expand the pattern and create a mathematical model...

Any thoughts and particularly any ideas would be greatly appreciated.

"Prop Lab"

Since I started teaching Physics I always wanted to have good labs. I tried the usual do this, then this, write down this bit of info... Every lab report turned out the same. The only real variety came from the very best and the very worst students. Not exactly best teaching practice.  Not to mention they were painful to grade. And what were my students learning? How to follow directions? Yeah, that's what science is, following a recipe.

When I started doing "Prop Labs" I was sold on the idea. I can't claim to be the brain behind the idea, I can only claim to be a groupie gulping the kool-aid. The idea is to give the students a "prop" and then let them have at it. The goal is to let them create the research question, let them create the procedure and let them figure out how to process the data and draw a conclusion. It's also most like real science! Don't get me wrong, I provided scaffolding in terms of general brainstorming and giving approval on questions so as not to "waste" several days. I also wrote a lab guide and modified old IB rubrics to help guide them through the details. The ideas kids come up with are often ideas I'd never think of. Now that's real science.

In the past I've given them props such as magnets, springs, rubber bands, balloons, clay, electric motors and vernier probes. If I can think of 7-8 solid ideas for a prop then its probably a good prop, if I can't come up with no more than 5 then its probably a no-go, however sometimes I'll give more than one prop which can make use of a just "okay" props. In the past student ideas for clay have included:

• Drop height vs. dent diameter in a sphere of clay
• Temperature vs. dent diameter in a sphere of clay
• Coefficient of friction vs. temperature
• Resistive force (to a string pulling through the clay) vs. temperature

The first time a class does a prop lab, they look at you like your crazy, like your asking them to do the impossible. By the second or third time around they're in the groove and chugging along. Pretty awesome, but you do have to be prepared for the push-back. 

The outcomes are not always stellar, but most of the class, at least 80%, come up with great ideas and are able to gather interesting data and draw a conclusion. Its amazing. 

Floating and Sinking

I never really thought of floating and sinking as a physics topic until I saw it done up at MSU in Bozeman in the introductory physics classes. Sure seemed pretty simple... Oh boy was I wrong. It was consistently the unit that gave people fits. While I don't want to drag my students through something hard for the sake of being hard, I do think a challenge is good for them.

So this year my class is cruising along much faster than last year so I'd been thinking I'd toss in some floating and sinking to occupy a week or so of class. It's something that they have experience with, that is assuming they've been in a bathtub or swimming pool before.

When I saw that the PhET folk had created a floating and sinking simulation I was sold on the idea.

http://phet.colorado.edu/en/simulation/buoyancy

The simulation does just about everything I would want it to do. It allows you to use 4 or 5 different material blocks and allows a continuum of densities for the fluid. It also comes with 2 scales, that can be moved, and function in the water and out of the water.

I did my usual which is to have the students work through some guided inquiry type questions. Seemed to work great for most, a few hiccups here and there. The questions could use some refinement, but in the end they picked up on the two main ideas. That is that floating objects displace their mass in water. Sinking objects displace their volume. That's good a start as far as I'm concerned.

Going where?

Lately, I've been a bit quiet in terms of posts. We had been preparing to go to an international job fair...

Its finally over. We accepted jobs 48 hours ago and I'm still recovering from the stress of the fair. Holy cow. It went great, so much better than two years ago, but it still aged me a good bit. Now the challenge is to stay focused for the last 4 months of the current school year. Could be tough.

The new spot is as a pure math teacher. No physics. The upside is it's IB Math, which I've taught before, but only the lowest tier. So it'll be great resume padding, not to mention a fun challenge. Hopefully some (IB) physics classes will come my way over the next year or two in addition to the IB Math. 

WYSBATDOKWYAD

Its not a new idea, but one I stumbled onto in some reading, that is telling the kids what they should know when they're done with an assignment. Thus the WYSBATDOKWYAD. In my physics class I have moved to a once a week homework with any suggested reading and other reminders listed on top of a print out. As an added bonus the paper has enough space for the students to complete the 3 or 4 problems from the textbook. 


Sometime in the middle of the first semester I started adding the WYSBATDOKWYAD.  The long acronym was mostly a joke, but it worked. The students got a laugh out of it and now remember what it means, if not word for word at least they've got the gist. So what does it mean? 

What You Should Be Able To Do Or Know When You Are Done.

I offered up extra credit if a student could improve on the acronym. So far I've only had a few weak attempts but nothing good yet...

More cars

This week in physics I wanted to introduce the idea of impulse as a stepping stone into momentum. I wanted to make a connection between work and impulse and the idea of force over distance and force over time. So out came the ramps and the cars again.


I had them do the following (I gave them some hints not shown):

1. Create a mathematical expression that relates the the amount of time a force is applied to an object of mass and the velocity of that object. 
2. Using the ramps and toy cars from before break. Collect 4-5 data points,the data should agree with your answer to #1.  If they don't agree figure out why and adjust.
3. Put your group's result on the board. 

No fancy equipment needed.

The results weren't quite so magical as before, but they figured out an expression for impulse (but didn't know its name) and gathered data to back up their pencil and paper work. What more can you ask for?

You can almost smell the learning.

In retrospect some of the hints I gave could be removed and allow a little more true inquiry.

The complete document can be found as a google doc.

Playing with cars

A few weeks before winter break I wanted to introduce the idea of energy. I usually do this with some boring chalk and talk about how we can use energy to solve more complex problems in a much easier way...


While that works, I'm not sure I get much more buy-in than just filling the chalk board with definitions and equations. Okay maybe that's not quite true, but it feels that way.


This time I decided I wanted to do a little exploration get the kids to figure out something on their own about energy. So as a class we took a short field trip to the maintenance building and got some old gutters and long planks of wood. I let kids (in groups of 3-4) pick their own toy car. I managed to pick up two 5-packs of hotwheels for $10 at Target. I also picked up some $1 slinkies that have yet to find a use...

Finally, I posed 3 questions to each group, the first two just being scaffolding for the last question, and then just got out of the way.

1. Given initial conditions of your choice, what is the speed of the car at the bottom of the ramp (or just off the ramp)?
2. What do you have to do to double the speed of the car at the bottom of the ramp? Triple?
3. What would you have to do so that the car had a final speed of 100 m/s? A theoretical question. 

I was trying to get them to model the idea of velocity squared being proportional to the height above the ground. Thus the length of the ramp and angle are secondary to height. And poof, with a little teacher voodoo the kids would have discovered gravitational potential energy... Well, it was so much better. 

They grabbed stopwatches and meter sticks and went to town. The kids got stuck on number two. One section nailed it during the first period. The other had 3 groups and all 3 got different results. I fought that teacher response of "well the answer really is..."  and said almost nothing. We decided to take one more class period to build a longer (6 meter) gutter ramp, some of the problems were  in measuring the time (we don't have any photogates). The kids spent 45 minutes experimenting and writing down numbers until the whole group saw the pattern! It was hands down the best class period of my career. 

In the end both class periods saw that the height was the determining factor, this required some guiding questions (Jedi mind tricks), and saw that there was more to figuring out the speed of a car than using kinematics and FBD's... There might be something far easier to use.

The handout I gave me students can found as a google doc.

What Santa brought me.

Santa brought a new toy for me this Christmas, one I didn't think I had much of a chance to get. I made my case as to why I should get one. But I thought my plea might have been ignored. Its not something that I really needed. Though I have used it a lot (I'm using it now). My friends and students are envious though I'm not sure they'd all make use of it...

What is it you might ask? A new bike? A new pair of skis? Nope. Just good old nerd candy. A new laptop. A free laptop from Google, a Cr-48 to be exact... And yes I said free.

For those who haven't heard Google has been working on an operating system based on their browser Chrome. Thus the name Cr-48. There's not much to it, which seems to be the point. Google was also very clear that the product was not going to be perfect, but that it was giving them out as a trial...  You can find all kinds of nerdy tech details on the interwebs. You can even still apply to get one for free, I'd guess teacher folk have a darn good chance at getting one.

When I heard about the new computer my internal geek wanted one. I realized it could be a pretty nice 1:1 laptop solution for schools. The computer would likely be cheap, they are not for sale yet or maybe not ever, its a lightweight processor, no hard drive, no CD or DVD, but it does have wireless and 3G. The fact that they are cloud based means if a student breaks one they simply have to pick up another and log-in again to have their files back. No more long wait times for the server to push the files down... I had this problem at my first school. The quick start up time matched with the 8-9 hour battery (no typo there) means it could work great for students going from one class to another all day long.

There is no desktop, no real way to download programs or games and thus no way to get a virus or download something that will ruin the performance of the computer as so many of my former students did. All the programs you can run are online apps from the Chrome App Store that work in a browser tab. I already use Google Docs and Sites for most of my school work. I realized a few months back that virtually all my time in front of a computer was doing work in a browser. I do my grades in a browser, I create class materials in a browser and I have become addicted to Google Reader after Dan Meyer mentioned it in a post. It seems like the Cr-48 was a near perfect fit.

The jury is still out. But if Google keeps working on the OS they might have something. For me they need to figure out the printing. I haven't played with their CloudPrint but I don't think its going to work for me, based on what I've read. My other major concern is the lack of support for Vernier probes. I need Vernier probes. I'm sure Vernier is capable of making a cloud based Logger Pro, but its not there yet and that's a problem if the Cr-48 is to be a viable 1:1 solution. There is hope as there is a single USB port...

I also miss my music. There are online solutions, but I haven't gotten that deep into the Kool-Aid just yet.

The Cr-48 is also not capable of running some of the Java based simulations from the PhET folks. As those require a file to be download and installed (I never liked that anyways). It does run the Flash based sims, but maybe a bit sluggishly (I've only tried one so far).

There is great potential...

Knocking off the rust with a little geometry

We start back to classes tomorrow. My precalculus course stopped mid-trig identity before the winter break.... We had talked about the reciprocal functions and the inverse cosine and only hinted at more identities.

I am determined to not teach as I was taught and to provide many different ways to see connections. I'm pretty sure that students learn better when I'm not in the way (How can you say that in an interview with out sounding like a lousy teacher?). When they can discover something on their own they remember it, they believe it and maybe they begin to get what I missed in math class. The beauty of patterns and logic!

I had been searching for a way to both review a little and to make all the trig functions real not just some arbitrary function I might write on the board. So I went back to geometry, geometry I never saw in class, so its new and fun for me. I'm not sure my teachers ever saw it either, but its possible that I was face down drooling on my desk in boredom during that part of class...

I had seen the picture below a few times but never stopped to really look at it.

Taken from Wikipedia

I had been thinking about this picture for a while. It seemed to me like a perfect review while learning something new. There might even be a few light bulbs going off "hey my, teacher didn't totally make up those functions!"

I created a quick "worksheet," how I hate that word, that guides them through some review of basic right angle trig, the unit circle and finally gets them to the conclusion that the reciprocal functions have a geometric reality! The intent (and hope) is that I can just get out of the way and let them learn in small collaborative groups. The magic seems to happen when they don't need me, just some questions to guide them...

The worksheet can be found as a google doc. (Still needs a little polish, but writing this was good procrastination.)