Thursday, January 10, 2008

Online and Free Calculators and CASs

I made a couple of minor edits to my Wiki page about online basic calculators, scientific calculators, graphing calculators, CAS systems, and plotting utilities today.

It still blows me away how much is available online and how good the quality is. Yacas (yet another CAS) has a tab called My Yacas that provides quick access to the list of commands and to the actual CAS engine - no download required.

Now, if only math students had the kind of access to computers and the internet that would allow them to use these tools routinely in school.

Update: Don't miss the link above to the actual page listing online calculators, CASs, graphing utilities etc.

16 comments:

terry said...

I don't know how teachers generally view calculators today. I suspect it is a mixed bag of good and bad. Certainly an over dependence on them is not good. The ability to do some degree of mental math serves as a double check on the correctness of a machine calculation - a reasonableness check. Not everybody needs to be Arthur Benjamin either - http://www.ted.com/talks/view/id/199 .

When I was in elementary school is was very bad at my academics - and arithmetic in particular. At the end of grade 8 I couldn't multiply worth beans and division was worse.

That summer I bought a calculator. I played with it for hours - and not just the 'shell oil' type of playing. I learned how to use every button on that thing and went through the manual - which was a mini math textbook. I spent hours calculating the slopes of lines around the house. Then I moved on to the slopes of curves; Later I would discover that it would be more properly referred to as the slope of a tangent line ;-)

Soon I was plotting the slopes of tangent lines, and then their slopes, etc. I even figured out what the formulas where for them in a general sense. I did a similar thing with areas. Later I would discover that I was doing calculus.

Then came grade 9 and math looked entirely different to me. That calculator had changed the course of my life.

Ross Isenegger said...

Thanks for sharing your story about your introduction to a calculator. It is interesting on so many different levels and raises some questions in my mind.

What is the relationship between arithmetic fluency and mathematical proficiency? One of my colleagues has one of the best mathematical minds that I have encountered and yet does calculations like 16+8 on a scratchpad next to him.

How do teachers take advantage of a compulsive interest like you developed and the resulting epiphany that you experienced? or are these best left in the realm of the personal?

Did the calculator change the course of your life or would that latent interest you had get spurred on by some other development? If it did, what tools and experiences must we get into the hands of students to unlock such discoveries?

My eldest daughter has been really good at Math all her life. Your story reminded me of the times when she was two and would skip count on a simple four function calculator while sitting on the potty. Later, when about 10 she could perform hexadecimal multiplication without the aid of a calculator. Now, at 18, she shows little interest in graphing calculators, CAS' or other impure devices, though I am fascinated by them.

terry said...

Arithmetic versus mathematics. Although my current day arithmetic skills seem to surpass that of the typical retail sales clerk, I still consider my arithmetic to be weak. I have a degree in mathematics, not arithmetic.

My father finished grade 8 about 1934. For him typical math skills included adding a page full of 5-digit numbers. I would think about that for about 0.03 seconds before firing up Excel. What we value changes as our tools change.

Compulsive? Hmmm, maybe I should seek counseling. In my specific case - the sea change was during the summer between grades 8 and 9. The teachers wouldn't have had a clue. As I think about Mr. Allan and Mr. Cooke - the two teachers who provided most of my high school math I can see that they recognized something. We have one computer in the school - a PET. I seem to have gotten a disproportionate share of it's time - something I never thought about till now. Thanks Mr. Allan.

Mr. Cooke - who also taught physics - was real mean and nasty. He picked on my work relentlessly. He was not fair at all. If I forgot a unit after a number or skipped a step in a worked problem he would dock marks. Other students (with lower marks) got away with mathematical murder - they could make glaring errors - skip steps and come close to the right answer - maybe and get a decent mark. I got no forgiveness - at least it seemed that way. Thanks Mr. Cooke.

The calculator was pivotal - it made my poor arithmetic irrelevant. I could do the math without being able to do the arithmetic. Perhaps I would have been better off if my early elementary teachers had taken care of that. For some reason I was considered not very smart and couldn't do any better.

For teachers today, yes tools can help, but I think the real key concept is that you give your kids a chance to change.

Ross Isenegger said...

"Give your kids a chance to change." - sounds like good advice for teachers, parents, employers and maybe everyone. I have often thought it odd that many teachers, who are supposed to believe in human development, assume that people will not grow. I think of negative comments about administrators like "I knew him 10 years ago and he was a poor teacher then..." implying that the person could not have learned anything or become more effective in the intervening decade.

Regarding compulsiveness, it is a topic that I find intriguing. Is it a sign of intelligence or is it a fundamental human characteristic? What do you say about the guy who collects pop can tabs for 20 years to build a life size replica of R2D2? Why do so many people become addicts to drugs, food or unhealthy pleasures - the nastier side of compulsiveness?

How do we as teachers appeal to students' interests in a way that engages them but not so much that they don't develop in other facets which are less interesting or natural for them - perhaps like Mr. Cooke did around rigor for you.

I am pretty new to blogging. Can you tell me how you became aware of this post in the first place? Has it spurred you on to subscribe to a feed? Do you use a feed reader? If so, which one? Do you have a favorite blogger that you read?

Cheers!

zac said...

Hi Ross

Not sure if you read 21st century computer algebra literacies when you were at my site.

You may wish to add your thoughts on that post.

Ross Isenegger said...

I posted a link to this post on a Math forum which is generating a lot of traffic, but not much of it is then going to the actual wiki page linked above: http://mathfest.wikispaces.com/Online+Calculators which actually has the information and links to all the really cool content.

zac said...

Hey, Ross - I visited your wikispaces page (this time in more depth) - thanks for a great resource!

Ross Isenegger said...

After seeing someone visit this blog as a result of searching for "Shell Oil", I asked Terry what 'shell oil' type playing with a calculator was. He said:

You know the algebra problems using words like
DOG * CAT = FIGHT
Find all solutions?

SHELL OIL type games are the same idea except done with a seven
segment display calculator turned upside down. SHELL OIL is 710 77345.
It has variations based on the calculator - some HPs had diagonal
lines in the display so you had a larger alphabet.

If you google "shell oil calculator math" there is a list of possible
words on yahoo answers.


and so there is. Although this post comes up first in the results. See the answer to the Yahoo Question.

I seem to remember having a book that had some of these in it early in my teen years. Maybe the manual for my first TI calculator.

Anonymous said...

I had the book also. I think it's buried in my basement somewhere

Tim said...

I have recently discovered this online CAS calculator:

http://www.vroomlab.com/nhome

click on the calculator image will let you access this virtual CAS calculator without login in.

I have since dumped the TI-*s and and all other scientific calculators

Ross Isenegger said...

@tim Thanks for the link. I have added it to the wiki page. There have been several additions (by me and others) since this post was made. I have heard from teachers who are using free iPod apps instead of TI calculators as well. Of course, Wolfram Alpha provides months of interesting exploration as well.

Tim said...

Hi Ross, you are welcome regrading the link to Omega, the virtual CAS calculator. I would like to suggest
that you change the link to:

http://www.vroomlab.com/nhome

instead of http://www.vroomlab.com/omega/omega.jsp?displayPage=c.jsp

The current link on wiki takes the user to a login page.

-Tim

Ross Isenegger said...

@tim I changed the link. You don't require a login once you visit the page that you gave me. There doesn't seem to be much information to indicate why the CAS seems hard to find and use. There is information at http://www.omega-math.com/Omega_Introduction.html that seems to imply that they would like you register for a trial. Is that what you did? I am left wondering if it will be freely available for much longer.

Tim said...

Hi Ross, I saw your change. you are on it!!

I never registered.

I had several email exchange with omega's developers recently and asked the same question you have.Their answer is that OMEGA TRIAL WILL ALWAYS BE THERE AND IT WILL ALWAYS BE FREE. They do plan to establish a site sometime in the future that requires registration.The new site will be supported by different hardware than the trial site and thus will have better performance. I did some digging and found that they have already set something up at:

http://www.vroomlab.com:8081/omega

which seems to be linux based.

-Tim

Anonymous said...

I have found a quick reference card for using Omega CAS calculator:

http://www.vroomlab.com/nhome/qr.html

Ross Isenegger said...

I have added a link to the wiki page to the quick reference card. Thanks for the heads up. Anyone is welcome to edit the page (and then watch how I fix it!)