Mathematics Add-In for Word and One-Note

Maybe it’s old news to you, but I recently downloaded the Mathematics Add-In for Word and One-Note (download from Mircrosoft for free, right here). It works with Microsoft Office 2007 or later. It’s a super quick and easy installation–doesn’t require a reboot or anything. I was even able to install it at work on my locked-down limited-permissions account without needing administrative privileges.

I’m impressed with its ability to graph, do calculations, and manipulate algebraic expressions using its computer algebra system (CAS). It’s not as powerful as Mathematica or my TI-89, or even other free CAS like WolframAlpha or Geogebra (yes, Geogebra has a CAS now and it’s not beta!). But I like it because (A) my expectations were low and (B) it’s right inside Microsoft Word, and it’s nicely integrated into the new equation editor, which as you know, I love.

sample output

Here’s some sample output in word format or pdf (the image above is just the first little bit of this five-page document). All of the output in red is generated by the mathematics add-in package. In this document, I highlight some of it’s features and some of it’s flaws. The graphing capabilities aren’t very customizable. And the mathematics is a bit buggy sometimes.

All in all, despite its flaws, I highly recommend it! It’s really handy to have it right there in Word.

TI Calculator Emulators

Online Emulator

Check out this online TI-83 Plus emulator! This just came across my radar from Hackaday.

It requires that you upload a (legally acquired) rom, but once you do, this seems like it would be a very good ‘on-the-go’ resource for presentations, teaching, or just any other time and place when you might need at graphing calculator.

I don’t have a TI-83 plus rom lying around, and I tried a regular TI-83 rom (which I did happen to have) but it didn’t seem to work for me. Hmm.

Mobile Devices

[updated] I now recommend Wabbitemu as the best emulator on the computer and for Android devices. It accepts a very wide range of rom files and has a nice feature set. The whole process is pretty user friendly. Here’s a link to the app in the Google Play store and here’s their website where you can download the desktop app.

Another great emulator for Android is Andie Graph which can be obtained in the following way (instructions come from our student, Jim Best):

  1. Download the app “Andie Graph” on your market for the phone
  2. Go to this link on the phone to download the ROM.
  3. There will be ads promoting other products so click on the bottom link that says DOWNLOAD.
  4. Once this has finished downloading, Run “Andie Graph”
  5. Go to settings by pushing the little icon on the phone itself that looks like a garage door or a tool box.
  6. Go down to ROM and select the ROM you downloaded. If the app doesn’t find the ROM, then you can search for it from the app in the phone.

Jim also suggests this calculator if you have an Apple product:

There is an app that is a type of TI-83. It is called RK-83 on the app store for apple products such as the iPhone and iPod touch. This is a $0.99 app that has the same functionality as a TI-83. It does not have the best of reviews but for $0.99, its worth a shot. There is also an app by the same creator that has better reviews but it is an 89.

Of course, there are scads of other great calculators out there if you’re willing to give up the look and feel of the TI experience. Desmos is a popular choice and works nicely on all platforms but isn’t a powerhouse of a calculator.

Plain-old Software

And as far as plain-old desktop software goes, here are some great emulators:

I actually prefer the Wabbitemu and Rusty Wagner emulators to the TI-SmartView emulator, even though our school has purchased copies for all of the math teachers.

Rom Files

In almost all the above cases, you’ll need to obtain a rom file for the calculator you’re interested in emulating. This is like the brains of the calculator. The emulator is just the pretty buttons and interface that run on top of the rom.

To obtain the rom file for your calculator, follow the instructions at ticalc.org here. I actually preferred using the instructions here for my TI-84 Plus SE. You can create your own rom file, or you can try to hunt for a download somewhere. This page has a bunch of downloads, but it’s not comprehensive. Remember that, legally, you must own the physical calculator if you download and use one of these rom files.

Good discussions in the math blog world

Here are two blog posts I saw a few weeks ago. I’ve been following the comments with great interest, and the conversations have been fruitful. You should go check them out and join the conversation!

  • Critical Thinking @ dy/dan — Once again, Dan gives deserved criticism to a contrived textbook problem. Hilarious problem, and fun discussion in the comments.
  • Disagreement on operator precedence for 2^3^4 @ Walking Randomly — The title says it all, but it’s the first time I had ever thought about how 2^3^4 or expressions with carets should be evaluated. Note that it’s clear how 2^{3^4} should be evaluated. We’re just unclear on how 2^3^4 should be evaluated.

When will I get my school-issued iPhone?

I’d love to streamline the attendance/homework checking/gradebook procedures. It always seems pointless to me to have to write down homework grades and attendance, then reenter it on the computer. Some of today’s teachers are already using smart-phone applications for such tasks.

 

One slick app from gradepad.com

From an article on NEA.org by Tim Walker,

It was only a few years ago that cell phones were being banished from classrooms. As far as school districts were concerned, these devices’ reputation as tools for student distraction, mischief, and even harassment easily outweighed any possible benefits in the learning process.

Banning them was—and, in many districts, still is—the easy call to make, but as cell phones have become more sophisticated, powerful, and even more entrenched in students’ daily lives, a growing number of schools have decided to open the door to what are, essentially, mobile computers.

“Educators can’t afford to be behind the 8-ball anymore,” says Mike Pennington, who teaches world history at Chardon Middle School in Chardon, Ohio, and blogs about classroom technology at Teachers for Tomorrow, a website he co-founded with colleague Garth Holman. “Schools need to embrace mobile technology and mobile learning. Students live in this world. These devices belong in the classroom.”

According to some estimates, smart phones, and to a lesser extent tablets like the iPad, will be in the hands of every student in the United States within five years. And as more schools embrace mobile learning, the number of education apps—mobile applications that run on your smart phone—are skyrocketing.

(more)

The article goes on to mention a handful of apps that have classroom potential, including the one above, GradePad. I also liked the looks of Attendance. And one of the commenters mentions that similar apps are available for Android users as well (here). This is all very cool, in my opinion.

In fact, I have a dream…

I can imagine a time in the not-to-distant future when I walk around the room at the beginning of the period checking homework and taking attendance from a mobile device. I’d be able to see the seating chart, do random name calling, see student photos, and control my computer. If students were issued similar devices, I could have them post their work on the board, using their mobile device as a slate to operate the front board. And students would use their devices as calculators and text books as well, perhaps. All my grades, attendance data, student data, and seating charts would be synced with the network and with our online grade reporting system.

We have Promethean (“smart”) boards in the front of our classrooms, and that’s been nice. But I think having mobile devices in the classroom would be far more advantageous, revolutionizing the way we teach more than smart boards ever did.

Most of what I’ve said is already technically possible–the hardware already exists. One hurdle will be cost, of course. But the cost could be significantly offset if there was no need to purchase hard-cover textbooks (very expensive) or smart boards (also very expensive). Another hurdle will be getting networks, software, and network administrators to cooperate. For instance, our district uses multiple vendors and some of our key data systems aren’t linked, like they should be. Allowing mobile devices to connect to the school network and the internet, providing district-approved  & purchased software, and syncing the whole system with existing data systems would be a sizable task.

Three cheers for the future! 🙂

PEMDAS Problems

Inspired by this post at Education Week, by David Ginsburg, and a fruitful discussion in the comments, I thought I’d make my own post about the order of operations. I feel the need to do this because of my own experiences teaching Algebra 1 and correcting the habits of Algebra 2, Precalculus, and Calculus students. The problem is often with their misunderstanding of the ubiquitous “PEMDAS” approach to order of operations (parentheses, exponentiation, multiplication, division, addition, subtraction).

The classic example given by those who have discussed this before is an expression like the following. This example shows the problem with instructing students to simply “add then subtract”:

8-4+1

You can easily see that blindly following PEMDAS would give you an answer of 3, not 5. In reality, addition and subtraction can be done in any order, provided that you think of the expression this way:

8+(-4)+1

I have to constantly reinforce in my students the notion that the “-” goes with the 4. It owns it. That’s the right way to think of it, since subtraction (and division) are just shorthand for addition by the additive inverse (and multiplication by the multiplicative inverse). That’s right kids, subtraction is an illusion. The typical Real Analysis approach is to use the field axioms to define the properties of addition. Here they are:

  1. If x and y are in the field, so is x+y (closure).
  2. x+y=y+x (commutativity)
  3. (x+y)+z=x+(y+z)=x+y+z (associativity)
  4. There exists an element 0 such that 0+x=x for all x (identity)
  5. For each x there is an element called -x such that x+(-x)=0 (inverse)

There are almost identical ones for multiplication, and then one more axiom for distribution. Just listing the field axioms for addition  helps us in the discussion of order of operations. As I said above, subtraction is never really mentioned. We only later define x-y to mean x+(-y).

Similarly, division is an illusion. Or more precisely, it is defined in terms of multiplication. We define x/y to mean x\cdot(1/y).

The other important thing to notice is that addition and multiplication are binary operations, meant to be functions of two variables. So the expression x+y+z is defined to mean (x+y)+z=x+(y+z).

But the problems with PEMDAS don’t stop with multiplication and addition. There are many other issues with the order of operations as well. We lie to students when we just tell them they’ll encounter those limited operations in tidy situations. Here’s a perfectly legitimate expression with which PEMDAS would flounder:

-2^{3^2}+\left|\frac{2\sin{0}+3!}{2-\sqrt{9}}\right|\pmod{3}

The reason the expression is so difficult for PEMDAS is because PEMDAS doesn’t acknowledge the existence of other functions or grouping symbols, and ignores the possibility of nested exponentiation.

As another somewhat related example, I often have Calculus students who evaluate the following expression incorrectly (because they misuse their calculator):

e^{(0.05)(10)}

And some high school students at every level still struggle with evaluating these expressions:

  • -2^2
  • Given f(x)=-x^2+x, evaluate f(-2).

The wikipedia article on Order of Operations is very clear on all this, but I wanted to just highlight some of the common misconceptions. For more, feel free to check out that article. I’m in no way recommending that PEMDAS be removed from math curriculum, but that it be used with great care. And by the way, the expression above evaluates to 1.

 

Equations from photographs with new Casio calculator

Excerpt from wired.com’s gadget lab:

If you’ve ever looked at the curve of a hill, the cables of a suspension bridge or the arc of a coastline and wondered, “I wonder what function would fit that line?” — congratulations, you’re a nerd. And Casio has a surprising new calculator that will answer your question.

Casio’s new Prizm calculator is to the graphing calculators of my school-days as the iPad is to the slates we scratched on with sticks of chalk. It has a color, 216×384 pixel display, 16MB of memory, a USB-port, and will do all of your math homework for you….

Any graphing calculator will let you input an equation and show you the result. Casio’s Prizm does this in reverse. The color screen will display a picture, and will draw a line over the top of any shape you like. It will then give you an equation for this line.

If that wasn’t amazing enough, that USB port lets you hook the calc up to a compatible Casio projector to show off the results on the big screen….

$130, available now.

That’s pretty amazing. I’m not sure it’s the most important feature of this new calculator, but it does highlight the fact that our TI-83’s haven’t changed significantly in 14 years. It’s surprising, given the advances in every other area of technology. Why isn’t your TI-83 calculator three or four times smaller and 20 times more powerful than the TI-83 of 14 years ago?