## Thursday, July 27, 2017

### How To Part IIA 2017: What About Desmos?

How To Part IIA 2017:
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 few 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 try an online Graphing Calculator like Desmos

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 Desmos. Desmos is a great alternative to a handheld Graphing Calculator such as the TI 84C or TI nSpire CX CAS. I was going to try Geogebra too as it has some CAS capabilities, but Desmos was much more user friendly and powerful. Geogebra is great as a Geometer SketchPad, but Desmos is where it's at if you want CAS!

2017AB2a) Definite Integral
2017AB2b) Numerical Derivative
2017AB2d) Definite Integral

2017AB1c/BC1c) Definite Integral

2017BC2a) Definite Integral
2017BC2c) Definite Integral
2017BC2d) Numerical Root
2017BC2d) Numerical Derivative

PS, here's a shot from the traffic jam I hit going home after the graduation!
Have A Great Summer 2017!!!

Teaching With Technology,

Well, that's all folks,
A. Jorge Garcia

Applied Math, Physics and CS
2017 NYS Secondary Math PAEMST Nominee

TpT

## Monday, July 17, 2017

### How To Part IIA 2017: Pythonic Calculus!

How To Part IIA 2017:
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 few 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! This year I used Jupyter Notebooks on http://cocalc.com to write and interpret my Pythonic code using the Python 3 kernel!

The final YouTube ScreenCast is my 2017 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.

2017AB2a) Definite Integral
2017AB2b) Numerical Derivative
2017AB2d) Definite Integral

2017AB1c/BC1c) Definite Integral

2017BC2a) Definite Integral
2017BC2c) Definite Integral
2017BC2d) Numerical Root
2017BC2d) Numerical Derivative

2017 Pythonic Calculus Executive Summary!

PS, here's a shot from the traffic jam I hit going home after the graduation!
Have A Great Summer 2017!!!

Teaching With Technology,

Well, that's all folks,
A. Jorge Garcia

Applied Math, Physics and CS
2017 NYS Secondary Math PAEMST Nominee

TpT

## Tuesday, July 11, 2017

### How To Part IIA 2017: SAGE Computer Algebra System!

How To Part IIA 2017:
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 use a Computer Algebra System like SAGE or SAGECELL or COCALC?

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 SAGE on cocalc.com aka Sage Math Cloud. In a recent post I talked about using python on a stand-alone PC without Internet access for testing conditions. However, I don't think that using SAGE 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.

2017AB2a) Definite Integral
2017AB2b) Numerical Derivative
2017AB2d) Definite Integral

2017AB1c/BC1c) Definite Integral

2017BC2a) Definite Integral
2017BC2c) Definite Integral
2017BC2d) Numerical Root
2017BC2d) Numerical Derivative

PS, here's a shot from the traffic jam I hit going home after the graduation!
Have A Great Summer 2017!!!

Teaching With Technology,

Well, that's all folks,
A. Jorge Garcia

Applied Math, Physics and CS
2017 NYS Secondary Math PAEMST Nominee

TpT

## Monday, July 10, 2017

### How To Part IIA 2017: Good Old Graphing Calculators!

How To Part IIA 2017:
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 these capabilities are demonstrated in the ScreenCasts listed below using a TI84C and a TI nSpire CX CAS:

2017AB2a) Definite Integral
2017AB2b) Numerical Derivative
2017AB2d) Definite Integral

2017AB1c/BC1c) Definite Integral

2017BC2a) Definite Integral

2017BC2c) Definite Integral
2017BC2d) Numerical Root
2017BC2d) Numerical Derivative

PS, here's a shot from the traffic jam I hit going home after the graduation!
Have A Great Summer 2017!!!

Teaching With Technology,

Well, that's all folks,
A. Jorge Garcia

Applied Math, Physics and CS
2017 NYS Secondary Math PAEMST Nominee

TpT

## Saturday, July 1, 2017

### Computing In Math Class ... A Sad State Of Affairs In 2017 ???

Computing In Math Class
... A Sad State Of Affairs
In 2017 ???
What follows is an excerpt of an email I wrote recently. I was writing to a retired colleague who found he needed to retire as he had little to no support in his work bringing computing into the mathematics classroom. He met with resistance primarily due to excessive administrative adherence to Common Core Standards. Ironically, this all occurred at a high school not far from Silicon Valley! The result of all this administrative fervor was a damping of creativity in general and a diminished use of computing in particular by this great teacher! I found his retiring under said circumstances very alarming as he was trying to do what I am trying to do:
"Wow, sorry to hear that, MrX. I find little support for teaching math with tech in general, not to mention pythonically, as noone really understands what we are trying to do or, even worse, don't care enough to even try to educate themselves.
I remember over 20 years ago how much resistance there was when we were trying to introduce the graphing calculator. Now we can't get rid of graphing calculators for something better. Graphing calculators have become the end all and be all of computing in the mathematics classroom, I'm afraid. If I even mention improving the state of computing in math class, I always get a comment about how many graphing calculators we have. Most teachers just pay lip service to using tech and coding in class.
It's ironic just how little the current generation of mathematics teachers cares about coding and algorithmic thinking in the current atmosphere of "the hour of code" push to get computer science into the K-12 curriculum in every school in every state. I have supported the hour of code every year on Grace Hopper's birthday to recruit for AP CompSci. However, I'm worried that the hour of code is pushing the curriculum down people's throats that may not really be ready to teach it. Maybe the powers that be want to water down the discipline in order to get it into schools at any cost even for students of way too young an age?
I am also of retirement age but I refuse to be pushed out! I feel as if I've only just gotten started. I don't know how much longer I can plod on myself but I'll try a year or 2 more I think. I don't get a lot of support but I don't get active abuse. It's strange, when I started teaching, most math departments in my area (Long Island) had at least an intro computing course called "Computer Math" and some even had AP CompSci. I have taught said intro course for over 30 years and the AP course for nearly as long. So I'm sort of tolerated as that crazy mad scientist over there in the corner when I try to bring computing into the math classroom.
It's strange how over the years less and less math teachers have any interest or background in computing. I have trained a few teachers over the years to take over my intro course but they invariably get snatched up by other schools offering better pay and work conditions....
I started teaching High School in 1984. At that time there were 3 or 4 other teachers interested in computing in my dept. I wanted to teach at my current school precisely because the chairman installed his own minicomputer for said curriculum (GIMIX, a Unix knock off complete with dumb terminals, text consoles, BASIC, Pascal and even a text based Adventure game way before Linux was around). So I thought the future of computing in the math dept was bright. I was even encouraged to design and install the first PC Lab/Classroom upgrade. However, less and less teachers, as well as less and less students, showed any interest in pursuing such a course of study.
So, to conclude my rant, I'll say this: I feel your pain but I'm gonna try to carry on 1 year at a time. Next year I'll be adding a bit of Processing to my AP Computer Science curriculum to spice it up a bit. I'll also be using SAGE a bit more in my preCalculus courses. Unfortunately, I don't think I can do that with my AP Calculus class as these students need to be proficient in the use of Graphing Calculators when they take the AP Exam."

Generally Speaking,

Well, that's all folks,
A. Jorge Garcia

Applied Math, Physics and CS
2017 NYS Secondary Math PAEMST Nominee

TpT