Tuesday, August 2, 2016

Let's Dump Those Good Old GCs!


Let's Dump Those Good Old GCs!
(excerpt from recent thread on AP Calc Forum)
I love teaching AP Computer Science, but that's not what I'm talking about here. Our Honors Math students, at the very least, should be exposed to computing as it's used in upper level mathematics and science majors or professions. 

This area of study is commonly referred to as Computing Science or Scientific Computing. Many of my students go on to some of the Big Tech or Ivy League schools for a major in Engineering or the Sciences. In said fields students and professionals will be programming computers to solve their problems. These professionals may use a programming language such as Python, C++ or Java. More likely, they will use a mathematical programming environment such as MATLAB, Mathematica or SPSS. Alternatively, I try to expose my students to FLOSS (Free Linux Open Source Software) versions: Octave, SAGE or R respectively (we use Linux a lot).

These past couple of years I thought I'd replace the TI83/84 in my preCalculus classes. Since preCalculus is mostly a terminal course for Seniors (not Honors) in High School whereby a Graphing Calculator is not required (no Regents or AP), I thought this would be a great place to experiment. The classes took to this approach very well. These students even felt special and accomplished when they told their peers in other classes that they were coders! I did keep the coding to a minimum, however, using predefined functions in SAGE

Early in the year (Sept), I did use pure Python coding for Sequences and Series as the List Data Structure, List Comprehensions and For Loops are very easy to introduce here. Later on (June), we were able to build on Sequence and Series when we got to Reimann Sums. Here's a playlist from that course.

Many schools nowadays have a 1-to-1 program where every student and teacher use some sort of compatible device provided by the school. Some schools, like mine, give out Graphing Calculators to everyone at the beginning of the year like a textbook. This way, everyone can use the same technology in class and at home. Some schools give out Tablets, unlike mine, whether it be an iPad or an Android, and use an app like Desmos or Geogrbra or even a TI Emulator. Don't forget, there's always a "App for that" or that "Droid does!"

Why not leverage the devices we already have? Most students and teachers have a Cell Phone or Tablet capable of coding with an online IDE, an app or a computing environment such as SAGE! As you can see from recent posts to this blog, the amount of python coding needed isn't much or hard to learn: 


Python, Sage or GC!

Of course, you could get a little carried away and teach a lot more (see the side panels of my blog for SAGE samples from all of the topics in preCalc and AB Calc).

I let my preCalculus students use SAGECELL in class and at home without a problem. I also let students use their own TI83/84 if they have one and prefer to use a Graphing Calculator at times as a mater of taste. I do not expose my AP Calculus students to any of this until after the AP Exam as they need to use a Graphing Calculator on the exam. Take a look at any playlist on my YouTube channel labeled "LAC" (Life After Calculus) for examples of what we do after the exam. 

Using Python in SAGECELL or REPL or VPython in GlowScript very easy to use and teach. These environments are to python as Processing and OpenProcessing are to Java. So, I may use Java in Math class too!

I was one of the first to promote the use of Graphing Calculators back in the early 1990s. Everyone was resistant to change back then. If a particular technology were not required on a particular exam, I think more people would be receptive to change now. Why saddle our kids with outdated tech that costs about $100 per calculator when they already have a ton of tech in their pocket or backpack?


Thanx,
AJG

Well, that's all folks,
A. Jorge Garcia
Applied Math, Physics and CS
2015 NYS Secondary Math PAEMST Nominee


Teaching with Technology, 
PasteBin SlideShare 
Sage Ebay
TpT

Friday, July 29, 2016

How To Part II 2016: Good Old Graphing Calculators!

How To Part II 2016: 
Good Old Graphing Calculators!
We just had our Graduation Day at the High School. I suppose that's my unofficial start to Summer. I will miss my Seniors, we had a great year together. The whole week before graduation I was finishing up a series of YouTube ScreenCasts about solving this year's AP Calculus Exam Part IIA. This playlist serves as a summary of this year's Final Project! 

Part IIA is the first Free Response section of the AP Calculus Exam. This section consists of 2 AB or 2 BC questions requiring the use of a Graphing Calculator. AB1 and BC1 are the same question. AB2 and BC2 are different. Below you will find the solutions to these Free Response Questions in the following order: AB2, AB1/BC1, BC2. In this fashion, we covered AB only questions first, then AB/BC questions and finally BC only questions, ie in order of increasing difficulty.

For over 2 decades, I have been teaching my students to complete this section using a TI89. Most schools still use a TI83 or TI84. These past 2 years, my students have been using a class set of TI nSpire CX CAS graphing calculators that were donated to my classroom via DonorsChoose. Thanx to all my donors, my students are indeed very fortunate!

There are 4 functions a Graphing Calculator needs to perform to be allowed on the AP Exam: 

1) Graphing in an arbitrary window, 
2) Solving for the roots of an equation, 
3) Finding Numerical Derivatives and 
4) Finding Definite Integrals. 

All of these capabilities are demonstrated in the ScreenCasts listed below using a TI84C, TI92 (similar to TI89) and TI nSpire CX CAS:




2016AB2a) Numerical Derivative
2016AB2b) Numerical Root
2016AB2c) Definite Integral
2016AB2d) Definite Integral




2016AB1c/BC1c) Definite Integral




2016BC2a) Definite Integral
2016BC2d) Definite Integral

PS, here's a shot from the traffic jam I hit going home after the graduation!


Have A Great Summer 2016!!!


Well, that's all folks,
A. Jorge Garcia
Applied Math, Physics and CS
2015 NYS Secondary Math PAEMST Nominee


Teaching with Technology, 
PasteBin SlideShare 
Sage Ebay
TpT

Tuesday, June 28, 2016

How To Part II 2016: SAGE Computer Algebra System!

How To Part II 2016: 
SAGE Computer Algebra System!
We just had our Graduation Day at the High School. I suppose that's my unofficial start to Summer. I will miss my Seniors, we had a great year together. The whole week before graduation I was finishing up a series of YouTube ScreenCasts about solving this year's AP Calculus Exam Part IIA. This playlist serves as a summary of this year's Final Project! 

Part IIA is the first Free Response section of the AP Calculus Exam. This section consists of 2 AB or 2 BC questions requiring the use of a Graphing Calculator. AB1 and BC1 are the same question. AB2 and BC2 are different. Below you will find the solutions to these Free Response Questions in the following order: AB2, AB1/BC1, BC2. In this fashion, we covered AB only questions first, then AB/BC questions and finally BC only questions, ie in order of increasing difficulty.

For over 2 decades, I have been teaching my students to complete this section using a TI89. Most schools still use a TI83 or TI84. These past 2 years, my students have been using a class set of TI nSpire CX CAS graphing calculators that were donated to my classroom via DonorsChoose. Thanx to all my donors, my students are indeed very fortunate!

There are 4 functions a Graphing Calculator needs to perform to be allowed on the AP Exam: 

1) Graphing in an arbitrary window, 
2) Solving for the roots of an equation, 
3) Finding Numerical Derivatives and 
4) Finding Definite Integrals. 

All of these capabilities are demonstrated in the ScreenCasts listed below.

However, in this blog post I wish to demonstrate that the use of a Graphing Calculator is, in fact, not necessary. Why don't we toss out the Graphing Calculators and just a Computer Algebra System like SAGE


I'm waiting for Doc Brown from Back To The Future fame to come by and say, "Calculators? Where we're going, we don't need calculators!"

Below you will find all my solutions using a Computer Algebra System called SAGE. SAGE is a free online Computer Algebra System hosted on Google Compute Engine that you can use with just about any web-enabled device! The 3 ScreenCasts below will take you through the solution of each Free Response Question step by step using SAGE.

BTW, you do need the Internet to use SAGECELL. In a recent post I talked about using python on stand-alone PC without Internet access for testing conditions. However, I don't think that using SAGECELL would be so bad for use in class even under testing conditions. The teacher/proctor should be able to watch what the students do during the test. 

I have my PC Lab/Classroom set up with all monitors facing the rear of the room. So the teacher/proctor can easily see that all students are on task at all times. 

Further, we administer a math placement exam at the local college. This placement exam is computer adaptive and is administered via the College Board website. We have had no problems using these PCs with Internet Access during testing conditions.


2016AB2a) Numerical Derivative
2016AB2b) Numerical Root
2016AB2c) Definite Integral
2016AB2d) Definite Integral


2016AB1c/BC1c) Definite Integral


2016BC2a) Definite Integral
2016BC2d) Definite Integral

PS, here's a shot from the traffic jam I hit going home after the graduation!


Have A Great Summer 2016!!!


Well, that's all folks,
A. Jorge Garcia
Applied Math, Physics and CS
2015 NYS Secondary Math PAEMST Nominee


Teaching with Technology, 
PasteBin SlideShare 
Sage Ebay
TpT

Saturday, June 25, 2016

How To Part II 2016: Pythonic Calculus!

How To Part II 2016: 
Pythonic Calculus!
We just had our Graduation Day at the High School. I suppose that's my unofficial start to Summer. I will miss my Seniors, we had a great year together. The whole week before graduation I was finishing up a series of YouTube ScreenCasts about solving this year's AP Calculus Exam Part IIA. This playlist serves as a summary of this year's Final Project! 

Part IIA is the first Free Response section of the AP Calculus Exam. This section consists of 2 AB or 2 BC questions requiring the use of a Graphing Calculator. AB1 and BC1 are the same question. AB2 and BC2 are different. Below you will find the solutions to these Free Response Questions in the following order: AB2, AB1/BC1, BC2. In this fashion, we covered AB only questions first, then AB/BC questions and finally BC only questions, ie in order of increasing difficulty.

For over 2 decades, I have been teaching my students to complete this section using a TI89. Most schools still use a TI83 or TI84. These past 2 years, my students have been using a class set of TI nSpire CX CAS graphing calculators that were donated to my classroom via DonorsChoose. Thanx to all my donors, my students are indeed very fortunate!

There are 4 functions a Graphing Calculator needs to perform to be allowed on the AP Exam: 

1) Graphing in an arbitrary window, 
2) Solving for the roots of an equation, 
3) Finding Numerical Derivatives and 
4) Finding Definite Integrals. 


All of these capabilities are demonstrated in the ScreenCasts listed below.

However, in this blog post I wish to demonstrate that the use of a Graphing Calculator is, in fact, not necessary. Why don't we toss out the Graphing Calculators and just learn a little bit of coding? 


I'm waiting for Doc Brown from Back To The Future fame to come by and say, "Calculators? Where we're going, we don't need calculators!"

Below you will find all my solutions using a programming language called Python. Python is a great first language to learn and use as it is very intuitive and powerful especially when solving math and science problems! 

The final YouTube ScreenCast is my Pythonic Calculus Executive Summary! This video summarizes everything we figured out in python related to solving Graphing Calculator Active Free Response Questions by coding instead! If you want a slower introduction to these numerical methods, please view the first 3 ScreenCasts. These ScreenCasts will take you through the solution of each Free Response Question step by step using python.


2016AB2a) Numerical Derivative
2016AB2b) Numerical Root
2016AB2c) Definite Integral
2016AB2d) Definite Integral

2016AB1c/BC1c) Definite Integral

2016BC2a) Definite Integral
2016BC2d) Definite Integral

Pythonic Calculus Executive Summary:
Includes plot() command!








PS, here's a shot from the traffic jam I hit going home after the graduation!


Have A Great Summer 2016!!!


Well, that's all folks,
A. Jorge Garcia
Applied Math, Physics and CS
2015 NYS Secondary Math PAEMST Nominee


Teaching with Technology, 
PasteBin SlideShare 
Sage Ebay
TpT

Monday, May 30, 2016

My Senior Cut Day Adventure 2016!

My Senior Cut Day Adventure 2016!
Last Friday was Senior Cut Day once more ... or, as I like to call this time honored tradition, Teacher Cut Day! I didn't actually cut, but I didn't do a whole lot of teaching either. As you can see above, I spent the day catching up on paper work as I also caught up on the last few episodes of Supernatural. That was between periods. During class time, if any Sophomores or Juniors showed up, we played BZFlag in Capture The Flag mode. We were all on one server with the left side of the room playing the Red Team and the right side of the room playing the Green Team. Fun was had by all!


What was even more fun was what happened the night before! I attended the BSHS Spring Concert. The Symphonic Band and the Orchestra are my usual favorites. However, I must say, the Choir stole the show with the help of NickB, MiguelM and DavidZ as seen in the video above from my Instagram.


Then, my luck held true, as I drove home after Senior Cut Day by way of the Ocean Parkway and Jones Beach. The place was jammed. There was no parking anywhere. I stopped by the side of the road, east of the Clock Tower, to watch the Blue Angels practice for the Air Show this Memorial Day Weekend! There were a lot of other air teams doing all sorts of stunts too as you can see in the Instagram video above.


Happy Memorial Day 2016!!!


Well, that's all folks,
A. Jorge Garcia
Applied Math, Physics and CS
2015 NYS Secondary Math PAEMST Nominee


Teaching with Technology, 
PasteBin SlideShare 
Sage Ebay
TpT