Sep 062015
 

In my Feedly this morning popped up the article by Larry Ferlazzo called, “Disappointing NY Times Article On Teachers & ‘A Sharing Economy’.” Okay, let me be more blunt. I am not disappointed in the NYT, I am frustrated and a little ticked off. It stems from this article in the NYT: A Sharing Economy where Teachers Win by Natasha Singer.

Read the article. I call foul AND shenanigans. How much did TeachersPayTeachers pay for this fluff piece that was nothing more than an advertisement for teachers selling out other teachers.

youblewit

Maybe it is because I am active and love the #MTBoS (that is the MathTwitterBlogo’Sphere, if you are not familiar with it.) I embrace the sharing, the collaboration and the freely giving of resources that the math teachers do on Twitter, their blogs and the internet in general.

The article should have been titled, “A sharing economy where teachers win, but collaboration dies.” Sure, some teacher just made $1000 by selling her lesson plans to a 1000 different teachers for a buck. She won, but collaboration died. Is she seeking feedback from people who have used her lessons? Is she improving them by discussing and talking about how others have used them? Probably not. It is in a store, and people are buying it. There is no reason or need to improve it.

Meanwhile, in the #MTBoS, teachers are making, sharing, improving and resharing lessons all the time. They are coming together to make better lessons. And then, they talk about these lessons, which spawn more, better lessons. This is a collaborative community where ALL teachers win, and more importantly, our learners win. And our learners continue to win. Over and over again.

Seriously, look at the amount of resources freely created and given away.

First up, websites created by teachers collaborating:

  • Let’s start with the MTBoS Directory. No one claims this is an exhaustive list. It requires teachers to add their names to it, but there are currently 344 teachers in the list, all with an online presence, and all sharing things.
  • Nixthetricks.com – created by Tina Cardone and teachers all over the #MTBoS who contributed tricks. You can download the most excellent book for free.
  • Fawn Nguyen’s Visual Patterns and Math Talks. Both are excellent sites. I have used the Visual Patterns site frequently in my high school classroom, and am working on learning more about Math Talks and implementing them in the college classroom where I am now.
  • Would you Rather Math is a site I used regularly in my teaching as well. Great questions, created by and curated by John Stevens.
  • Michael Pershan’s Math Mistakes. See an interesting math mistake? Submit it to this site and have a discussion on the thinking the learner made while making the mistake. We can learn more from mistakes than we can from correct work.
  • Dan Meyer’s Google spreadsheet of 3 Acts lessons. More on this to come. I am working on an idea taking shape out of my current position as a Master Teacher with a UTeach model school.
  • Mary Bourassa’s Which One Doesn’t Belong. So Mary saw Christopher Danielson’s great shapes idea, and realized that there was some amazing math thinking that could be done. BOOM, another collaborative website created.
  • Open Middle Dan Meyer introduced the idea, Nanette Johnson, Robert Kaplinsky and Bryan Anderson ran with and created the platform.
  • Desmos Activity Bank A site created by Jed Butler out of the need to share Desmos files, first showed at TMC15 at Harvey Mudd College.
  • MTBoS Activity Bank created by John Stevens (second time his name is on the list) to collect and curate some of the awesome materials created. Anyone can submit their own, and searching is easy.
  • The MTBoS Blog Search also created by John Stevens (I don’t think he sleeps). This site allows you search the blogs of a long list of math teachers for lessons, content, whatever you are looking for.
  • Robert Kaplinsky has a Problem Based Search Engine, to find those specialized lessons that are, you guessed it, problem based!
  • The Welcome to the MathTwitterBlogoSphere website has a further collection of collaborative efforts that includes some of the above but is even larger.

But that isn’t even all of it. There are teachers who are collecting curriculum, links or materials and sharing it all back out; lock, stock and barrel. These teachers have “Virtual Filing Cabinets” full of lessons that have been tried and tested, re-written and shared back out. Some call their pages VFC’s, some are just curated sites of materials.

And then there are great organizations giving away curriculum:

  • Illustrative Mathematics, free ever-more-complete curriculum that is CCSS aligned and incredibly high quality.
  • Shells Center/Mathematics Assessment Project, good as lessons, problems or assessments. I forget about this site until I am desperate, and then kick myself because it is just so good and thorough.
  • Mathalicious has free lessons and paid lessons. I have used them in class. They are worth paying for!
  • Igor Kokcharov has an international effort in APlusClick. Lots of great problems and lessons.

And this list is FAR from complete. It is what I pulled together in 15 minutes of thought. And this list does not even begin to talk about the 180 blogs

So, NY Times and Natasha Singer. You blew it. You didn’t show teachers winning, you showed teachers selling out. If you want to see winning teachers, click on any link above and read their sites.

The above are all winning teachers. TeachersPayTeachers is an example of teachers losing out on this kind of collaboration.

Oct 212014
 

My last post was in September and was entitled “I am tired so tired.” That ended up prophetic because with the fall break I ended up not posting for three weeks.  Whew. I needed that break to get back on track and then caught up. I am glad I have my head on right now and am refocused.

So, on to new posts.

Today, Eli Luberof posts on Twitter:

 

Yay! This was amazeballs! You should try it. If you don’t want to try it, I took a screencap of what Stats looks like in Desmos. Desmos 2     

 

This just made my day. Now I can do data entry, just make sure to use the subscripts on the data points and the variables. Notice that you can do different forms of the equations! You can do yhat = a + bx or you can do yhat = mx + b. Either format gives you the r value and the residuals.

Go residual plots! That is awesome in and of itself. I am in love. Right now, the only thing that kind of saddens me is that I can not use “height” and “time” as variables. Desmos needs the x_1 and y_1 format to work. That is sad, because in stats we try to use words as variables. Oh well. At least this gives me a clean, nice, clear way to teach this topic to all classes.

Eli, two thumbs way up for this addition. [And just as an aside to the rest of the #MTBoS to show how responsive Eli is to us. He did a small focus session at #TMC14 with several stats teachers and asked us how we would want to do this. He told us he had not thought about residuals at that time, so to see residuals so easily pop up here was very exciting. Desmos is truly responsive to teachers needs.]  

Edit: Okay, so I kept playing and tried to build a lesson with it on residuals. Found some interesting things that I like and don’t like. I tried to calculate the predicted values, the yhat. Desmos didn’t like merging the algebraic with  the regression. Not at all. This is what I got when I tried: Desmos 3                          

 

 

 

 

 

 

 

I would like to have the ability to show not just the actual value, but also the predicted value. That way I can show where the residual actually comes from. Beggars can’t be choosers though.                      

Edit again: Desmos comes through like a champ. They tweeted this out to me last night.  

 

Which led me to do this:

desmos4Click on it and look at it large. You can see how I used a function per Desmos’ advice to then calculate the residuals instead of just using what is given. This pretty clearly shows where those points at the bottom come from.

I am teaching residuals right now in AP Stats, and I will use this as a demonstration (if it is up long enough) to show what the calculators are doing. Too often the learners don’t think beyond the buttons and just mechanically find the resid plot without thinking about what is going on.

Aug 282014
 

Algebra 2:

mindblown

My learners blow my mind. I assigned my Honors Algebra 2 learners to write their name.

Seriously, all they had to do was write their first name.

In Desmos. With functions.

Heh, I am evil, right? It gets worse. They had just taken a quiz, so we only had about 10 minutes left in class. I showed them how to create an account on Desmos to save their work. I showed them how to type in a function. I showed them my name in Desmos. And then I showed them that if they scrolled down on the main Desmos page, they would see, well, they would see some amazing art created by learners like themselves.

That is it. That is all the prep, instruction, training, or anything else you want to call it, that I gave them. They had to take this bare bones instruction, write your name, and run with it. I never showed them circles, ellipses, or any other function. They learned it all themselves. Here are samples of what was shared with me:

skylar24 cloe10

Skylar = 24 functions, Chloe = 10 functions

 

janine35 gentry17

 

Janine = 35 functions and Gentry = 17 functions

Pretty representative. I did not say they had to use any special functions, just write your name. And I want to point out, I never showed them translations. They figured that out themselves by working with Desmos for ONE SINGLE DAY! Nice.

Then I started looking at the functions each person used. I noticed something very interesting that Chloe did. She only used 10 functions, but the “e” was especially interesting. You see, she did BOTH a domain restriction AND a range restriction on the same function.

cloeamaze

See what she did there? Mind Blown. I am still stunned by the creativity she used with Desmos. When I asked her why she did both her answer was, “I was just trying stuff until it worked and looked the way I wanted it.” Genius. Necessity is the mother of invention.

Anyway, we finished up by rocking translations. They already had the main part of translations down because they played with Desmos. That was awesome. They are still trying to make things complicated, but I am almost finished breaking them of the assumption things have to be difficult.

 

AP Stats

I am short 40 books so far this year, so I need to do things to get my learners doing problems without the book. One way to do that is Relay Cards. This is how I play the game. I hand out problem 1. Everyone gets the same problem, so they can discuss it, but they have to write their own.  I use a magnet to hang the answer I previously made on the board. The learners can come up and read the key after they have tried it. Their answer must be the same as my key in meaning, not in words (usually. Sometimes it has to be exact, as in the probability section.)

Once card one is done, they come to me for card 2, and so on.

Having the key on the board keeps me free to answer questions and help while I hand out the new problems and double check the accuracy of the previous.

I just finished a set for Experimental Design.  I have other sets (created by Shelli Temple (@druinok) almost completely).

03 Relay Cards for Conditional Marginal Probabilities

Ch 6 – Relay Cards – normal models

These are a great way to get the learners talking about the stats, writing and working with stats, and the teacher does nothing but help, coach, and assist learners learn.

I like this activity greatly.

Mar 072014
 

My goals:

  1. Construct a consistent vocabulary of problems that can begin in Algebra 1 and extend through to Calculus, Statistics, and all courses in between.
  2. The problems must have the potential to be engaging to learners.
  3. The problems must hit at least 4 of the eight Mathematical Practices & high school math standards (CCSS).

My idea started with this idea for Algebra 2: Model the escape velocity of a rocket on the Moon and the Earth. ( PDF and Word DOCX) This ended up being a far more difficult task than I expected, mainly because the learners did not connect the idea of writing the equation of a line with the fact we had a function in front of us.

I Desmosed the project for a visual display, and we spent another day discussing it and achieved the goal. [Is it okay to use the name as a verb? I don’t care, I am doing it anyway.]  It turned out great in the end, but it made me start thinking hard about how to connect Algebra 1 through Calc and Stats and make the ideas more real, more understandable, and more connected.

From there came the idea of using an “off the shelf” structure in a new or different manner to extend the lessons. Enter http://graphingstories.com . Dan Meyer started the Graphing Stories with a long time ago, and they are awesome. But they also fit the idea of using the video / graph combination to write the equations of lines and finding area under the curves.

With that in mind, I offer the following Desmos files:

File 1:

  1. This uses the Graphing Story of water being poured into a graduated cylinder to create the graph. I took some points from the graph on screen, and wrote a function that goes through the point (0, 0) because we know it was empty at time 0.
  2. Notice that the line does not go through exactly all 4 points! That allows for discussion of variability and observation skills.
  3. I also used the (h, k) form to write the function f(x) because it is the easiest way to show the line.
  4. What does the slope MEAN?  A standard AP Statistics interpretation is: As the time increases by 1 second, the water increases by 40.67ml.
  5. Next, find the area under the curve. Move the slider for “b” to the right and you see the area highlighted.  Okay, standard triangle, ½ b*h, and you get 5205.33 ml*sec. ??? What does that even mean?
    1. It is called “absement” and it is the time-integral of displacement. Yes, we don’t need to discuss that for Algebra 1, but as teachers we should know it.
    2. The area is the sum of all the instantaneous moments of water before. With the Desmosed file, you can see and clearly communicate what it means. It means that you are adding up the area of the little triangle when b=1 with the larger triangle when b=1.5, and then with b=2, etc. Except the area is the sum of the instantaneous areas, not the discrete areas.

Notice that this one lesson required the learner to interpret a real life action, pouring water, into a graph, and then find the slope and write the equation of a line, and then interpret the slope, and then find the area under the curve.

These are all essential skills of the Calculus learner, done at the Algebra 1 level!

A second one.

  1. Now we are removing cups from a scale.  There are actually several questions that the video brought to my mind, like is this really a continuous line, or should it be more discrete? Time is continuous, but the weights really are stepped.  But, I left it as is though because I wanted to not change it from what the video shows. That is a larger conversation in class.
  2. We now have a negative slope to calculate, which does not really make a huge difference for interpreting the slope: As the time increases by 1 second, the weight of the cups decreases by 3 grams.
  3. The fact the line only hits 1 point absolutely creates some conversation about which point to pick, variability, ect.
  4. The area gets fun, however.
  5. Notice that the FULL area is still a triangle. However, if you move the “b” slider across, you notice the partial areas, the area at 5 seconds, 8 seconds, etc, are trapezoids! Now the learner can be challenged and pushed to incorporate some extra questions of find the area of trapezoids.
  6. We still are doing and absement calculation and not a displacement calculation.

Finally, the Desmosed Lunar Modeling I started with:

It is far more complex and involved, but that is why it is an Algebra 2 lesson and not an Algebra 1 lesson.