I always thought mathematics at school was all about being taught a new language – one that helps us live in a culture built on numbers, enables scientists and engineers to understand and control the world we live in, and enriches us by revealing the underlying complexity and beauty of the universe.
I was wrong…
I now know that mathematics at school is all about learning to use a high end Texas Instruments graphing calculator.
I came to this revelation while purchasing my 12 year old son’s school supplies a couple of weeks ago. The supply list stated, and I quote,
“ALL Algebra I and Algebra I Honors are REQUIRED to purchase a TI-83 plus or TI-84 calculator”
(The emphasis has not been added – this is how it appears on the school’s web site)
The TI-84 Plus graphing calculator - every seventh grader should have one!
Back when I was at school, my math teachers had some funny ideas. They thought it was possible to do mathematics with a pencil and paper. They had this idea that equations could be plotted and solved using graph paper. And they adhered to the archaic notion that learning the language of math was more important (at that stage) than the actual numbers.
No wonder I’ve had such a stunted professional life as a scientist – unlike today’s enlightened education authorities (in the US at least), my teachers didn’t realize the absolute necessity of owning a graphing calculator.
I must confess, because of my ignorance, the penny didn’t drop when I first read my son’s supply list. Because I had been so sadly impoverished in my mathematical education, I assumed that these TI-gizmos were bulk standard scientific calculators. Oh no – these are top of the line Texas Instruments graphing calculators; the cream of the cream in the world of pocket sized number crunchers.
Conveniently, the local Staples store had a prominent display of the calculators, and boxes of them just waiting for parents eager to give their seventh graders the best possible math education. Very kindly, the store was also selling insurance policies to go with them – just in case your son or daughter lost or broke their beautiful new $100 purchase.
I must confess though, I was a little shell shocked by the cost and complexity of this algebraic marvel – probably because I hadn’t had the benefit of such a wonder as a child. So I did a little digging around as to whether this is a standard item in the young person’s mathematical education, or whether it was just a local thing.
I now know that almost every reader of this blog in the US who graduated sometime in the past 20 years or so will have had the advantage of a TI graphing calculator in their mathematical education.
Apparently, the TI-83 or (ideally) the TI-84 graphing calculators have been essential items in US schools for decades. There are even textbooks (so I’m told) that require these devices, and exams that are impossible to take without them.
Interestingly, it always seems to be the Texas Instruments calculators that are needed.
It was at this point that it hit me: This is where my life had gone wrong.
Up until now, I thought I had been doing okay. I had a good degree in physics. I graduated with a doctorate in physics from the University of Cambridge in the UK. I’d managed to do some reasonably innovative research over the years, publishing a few papers – although admittedly, only a handful have been in high impact journals like Nature. I even had a reasonable job.
But I had never had a TI-83 (or TI-84) graphing calculator!
For years, I’ve been under the delusion that a $20 scientific calculator is all you need to make it in this world, together with pencil and paper, and maybe a computer for the complex stuff. I can only imagine what heights I could have scaled, if only I’d of had a TI-83 from Texas Instruments!
My one consolation is that I’m not alone in this. Having become aware of this crippling omission in my professional life, I began asking colleagues about their own experiences. And here’s the real tragedy of this story – so many great intellects around the world have been held back it seems, because they never understood the importance of a good graphing calculator.
A senior research advisor in UK admitted to me just this last week to never having fathomed the relevance of these instruments. Another good friend and highly influential scientist was highly skeptical of these button-festooned pocket data plotters. Who’s to know—with a TI-83 graphing calculator, they could have been advisors to prime ministers, or Nobel Laureates!
In fact, I’m left wondering whether the mandatory use of TI graphing calculators in US schools has been the secret of the country’s mathematical success in recent years. I’m sitting on a plane while I type this, and so cannot check the figures. But I bet when I do it will be clear that, thanks to Texas Instruments, the mathematical ability of students in United States far surpasses that of other countries. Unless of course, TI have been generous enough to share this intellect-expanding invention with education agencies, boards and curriculum developers beyond US borders…
Fortunately, I now have a chance make sure my son has the advantages I never have. And there’s going to be no expense spared. I was tempted to buy him the cheaper TI-83 plus graphing calculator. But I gather from my research that the $120 TI-84 plus has a significantly faster processor and is the recommended choice by many.
It hadn’t struck me before that processing power is important when it comes to buying a calculator.
Now I know better.
Thank goodness for the internet for that piece of enlightenment – I could have ended up buying my seventh grader a real dud.
And thank goodness for Texas Instruments – today’s highly mathematically literate generation owes you. Big time!
I wonder what effect this supply list will have if/when math is an elective – I suspect it will mean some parents will be forced to guide their children towards other courses that don’t ‘require’ expensive supplies.
I’d hope it doesn’t push things that far. But in the current economic climate, $100 is a large chunk of change to fork out on a calculator that, in all honesty, is likely to sit mustering in your seventh grader’s locker. (my daughter took Algebra I last year, and barely touched a conventional calculator, never mind a graphing calculator).
My daughter goes to a school in Scotland and we have had exactly the same instructions to buy exactly that calculator. The really depressing thing about it is that I am unable to help her with her maths homeowrk (despite it being my best subject at school) as I don’t understand how to use the calculator.
That’s really sad Fiona – I hadn’t realized this dependence on graphing calculators had spread to Scotland!
This is a real problem when the actual process of using a particular calculator becomes part of the course requirement – especially as very few jobs later on will depend on this (and for those that do – how hard can it be to learn to use a calculator on the job?!). And as you say, it alienates parents who could otherwise help and encourage their kids to get into math.
I read you from France to obtain advice on Ti calculator.
Also here, we are fronting the same “need” of a Ti 82 to 83+.
I can ensure you give the best of all ! I don’t understand why a mathematic course could depend on calculator type. Ti shows a validation by the french educational ministry (which deal with american calculator, recommending them). And so far, no need of an HP or Casio, just Ti… ???
I recommend to buy a second-hand stuff whose owner now know that it had no use of.
Thanks again for your post.
See if he can use it to work out, with respect to carbon footprint, the equivalence point of sheets of conventional graph paper against full life-cycle impact of his calculator.
🙂
Ouch!
I must confess, going off on a tangent, there’s something about crisp, fresh sheets of quality graph paper that the fanciest calculator doesn’t get close to touching!
Hear, hear. And the sad part for us, after we had bought 2 of these machines for our middle school children, was that when our eldest got to high school she was told that she could NOT use it for her 9th Accelerated math class. And that is because a different, albeit simpler and cheaper TI device (Texas Instruments 30X-IIS) is required.
I have a nasty feeling we are going to be in the same boat here – I would love to hear whether the push for high end calculators is coming from the math teachers themselves, or from some far removed decision-makers in the various education authorities.
I just can’t seem to part with my slide rule. No LCD display, but it did give a graphical representation of what a log scale looked like.
I’m not saying I was ever any good with a slide rule, but I was rather proud of the ones I owned. The vinyl equivalent of today’s digital number crunchers?
I remember during the Apollo 11 mission that the NASA scientists and astronauts used slide rules and a guidance computer of very low power
http://historical.ha.com/common/view_item.php?Sale_No=669&Lot_No=25368
http://www.downloadsquad.com/2009/07/20/how-powerful-was-the-apollo-11-computer/
Now in 2010 there seems to be a problem in revisiting the lunar surface, not due to a lack of computing power but of finance.
I wonder what impact this will supply list when / if Mathematics is an elective – I suspect it will mean that some parents are forced to have their children in other courses, not its leader ‘require’ expensive care.
Great essay. I wholeheartedly agree with you. Unfortunately…I wasn’t aware of how entrenched graphing calculators have become even at the college level. Our local community college requires them for Advanced Algebra, Trig and all Calculus classes. And that trend seems to be expanding throughout the “higher” education system in the US. Which is why I dropped out. Better to learn it on your own and really understand it than just learn how to crunch numbers and punch buttons. I think this whole movement is simply about getting kids to pass math so our stats look good in comparison to other countries that do much better at math.
Thanks Mike,
There’s been concern now from people in industry and academia – and not just in the States – that kids are being taught how to pass exams, rather than actually do stuff! I suspect the prevalence of graphing calculators may possibly be a part of this problem!
I personally don’t know what i would do without my TI-83 plus, it has served me well on every math and science test since junior high and I am currently in my junior year of college majoring in chemistry.
Finally – someone standing up for the humble TI-83 plus – thanks bonez565 🙂
I’ve got to ask though, are you the sort of person that loves to play with gadgets, and do you use the graphing feature (as opposed to simply the other science calculator stuff) a lot?
I want to order a ti 84 plus calculator please deliver it at Gadebuscher Weg 4-6 Dahlem 14195 Berlin.
Always interesting when someone takes something unexpected from a blog! Sorry Ruth – I’m not selling Ti 84 calculators, but I’m sure a local store is!
When I took Linear Algebra at a local community college three years ago, the syllabus said that a TI-86 was required. I really wanted to use my HP-49G rather than buying another calculator. In principle the issue was that the instructor wouldn’t be able to help students who had the wrong calculator. In practice he seemed to have a hard time helping even the students that had the right one. I got by fine with the HP-49G, and didn’t need any help with it. I wrote my own program to find the nullspace of a matrix, though later I found out that the nullspace is also known as the kernel, and the calculator had a built-in kernel function.
I think the class would have been better if it had been done with no calculators at all. They weren’t allowed on the tests anyhow.
My niece is having trouble learning multiplication in grade school. I would be happy to help her, but they have some new way of teaching multiplication that is more complicated than the standard method, in order to emphasize the use of the distributive principle. It seems that the “new math” is making a comeback. I think it’s fine to spend a little time explaining to children why the standard procedures for multiplication and division work, but forcing them to do it all in a highly theoretical manner at that stage isn’t really helping them in any way. I think it’s all part of the plot by textbook publishers to get schools to buy new textbooks every 2-3 years. If we keep teaching things by the same method, we won’t need to buy new books until they wear out. I’m hopeful that the efforts to develop open-source textbooks will put an end to this madness.
Thanks Eric,
You touch on so many things – the joy of programming your own calculator, the frustration of working with inappropriate tools, the ever-shifting trends and fads in education (I also struggle with helping my kids with math that should be straight forward, because they are being taught convoluted methods), and the faint suspicion of profiteering in the education world…
Plenty of food for thought!
I have used calculators since University, from the HP28C to the current HP50G. However, they have always been a tool to help with the maths, not a substitute. I still write some programs, sometimes for work, sometimes for fun. It’s good to go to a meeting with just a calculator in hand and evaluate different scenarios or plot distributions – without dragging in a laptop, fiddling to connect it to a projector, fiddling with the power supply halfway throug because the battry’s going flat.
I worry that children learn to plug numbers in and just accept what comes out – not knowing if it’s even in the right order of magnitude. I’m not comfortable using a program or routine if I don’t know what it does. How else do I know the limits and accuracy? How do I know I’m using the correct program/formula for what I want – some have very subtle limitations.
And the whole TI thing – I suspect there’s some profiteering going on there somewhere.
Thanks Bart,
I should be clear that I’m something of a “good” calculator affectionado – I love my HP 22S scientific calculator (although purists would turn their nose up at it for not using RPN!). But as you say, it’s how you use them that matters – and that means knowing their limitations!
There’s a great discussion going on at the Museum of HP Calculators sparked off by this blog (just love the idea of a HP-calculator site responding to a blog on TI calculators…). Well worth checking out:
http://www.hpmuseum.org/cgi-sys/cgiwrap/hpmuseum/forum.cgi?read=160609#160609
Update 1/13/10 – Link is now dead – will try and find out whether MoHPC have archived the thread…
The links dead.
On a more pertinent note, I grew up using these calculators everyday since middle school and let me tell you, they were about the most useful piece of school equipment ever! Infact they were so useful that we used them in most classes and when we should have been doing my math homework. I mean, yeah my teacher said they did calculations, but she also taught us how to do those by hand and mind. Surely the reason they were a required purchase was because they were the only hand held gaming device that didnt distract other students in the class (mostly because we all had them and all the games so there was very little “oh! whats that game?). Actually these things did get us started on programing when we used them to create our own games and fake os memory cleared screens so the teacher could be deceived when they told us to delete our games. Man, I was bummed when we had to get rid of them in college and go back to the regular scientific calculators. It meant I couldn’t check my answers as easily any more but hey, this scientific has a algebraic solver. That still didnt make up for the lost games though. Man I miss Pimp Quest and Drug Cartel. Those were some of the most played games if you couldn’t get a TI-89 which had Pheonix.
There’s definitely some profiteering going on.
These calculators are what, basically early 1990’s technology (at best) that still somehow command a premium. These things have very low resolution monochrome screens and no backlighting. Look at what $100-$150 will get you in any other electronic device.
Furthermore, the TI 83/84 actually are missing many features found in other “obsolete” or lower powered calculators. For example, there isn’t really much more complex number support than the “i” on the keypad (as opposed to the complex matrix support on the TI 85/86), and they lack the pretty printing capabilities of the $15 TI 30XS.
Even some of the scientific come with basic algebraic solvers that these $100 behemoths lack. Many of us held little but scorn for our schools and/or school administrations. When I got to college, I was sadly lacking in the ability to do the things my father did mentally… because I forgot where the commands on the calculators were…
Dude, it’s no big deal. Learning a calculator isn’t the main focus of the class; the calculators are just there to help students see the graphs without wasting class time on drawing them. They’re also useful for finding intersections of graphs that would take a long time to figure otherwise (think Newton’s method by hand). I started using a TI-84 in 8th grade and turned out okay (Physics major as well). Don’t you think it’s better to learn more mathematical concepts per unit time than to spend time working calculations out?
Ha – I guess you’re living proof that you can get a decent education AND use a TI-84 🙂 Actually, there’s clearly a community that take to these things like a duck to water, and really benefit from them – good for them. But I’m still not convinced that they are a good learning tool – precisely because they can get in the way of getting to grips with underlying concepts and really understanding what the numbers are about. I my be old-school, but I still think there is tremendous benefit in drawing plots by hand – it’s a process that forces you to think beyond the answer to the reason you are looking for the answer in the first place.
I think Andrew’s concerns are legitimate. My first math class in college, about 14 years ago, I almost flunked a section of the class which required the use of a new, poorly written, math software program to solve the problems. Fortunately I did understand what I was doing and was able to solve these complex equations by hand, unlike some of the other students in my class. I think we were one of the first generations to be told we should buy a Ti-83/84. I never did buy one but I’ve always gotten along just fine with a $20 calculator, paper, pencil, Excel, and the odd specialty program. If you really understand what you’re doing with an equation you can solve it. While not everyone relies on advanced calculators to pass the class, a lot of people I knew did lean on them too much, which is probably why all the university math, chemistry, and physics courses I took, and later proctored, banned their use on tests. In that case the question becomes, what’s the point having a $100 calculator that you aren’t allowed to use on tests?
Programmable calculators are now available as iPhone/iTouch applications. One similar to the TI83 will save $99: http://www.piglit.net/pi83
(disclaimer: I have not used it so YMMV)
My preferred scientific calculator app in the iPhone is the Free42, an emulation of the HP42S: http://thomasokken.com/free42/
Note free 42s emulation for PC, Windows Mobile phones and Palm. I used all the above…
And in high school, I had tables, slide rule and a 4-operation calculator. My first serious scientific calculator was an HP67, 2nd year at university, at the time where the other choice was a mainframe computer. Very useful to solve some problems in my EE classes.
I really like the apps now available on the iPhone/iTouch – but they’re not allowed in schools! In Fairfax County VA, they are locked into the IT calculators – in principle, kids are taught how to use this specific calculator, rather than how to use calculators in general!
Andrew Maynard: Respectfully, sir… I think you missed the point of your own anecdote! The Texas Instrument graphing calculator is today’s slide rule and graphing paper. Students today should be learning Matlab or Maple. Our brightest students are being forced to use tools (TI-83+) that stunt, rather than foster, intellectual growth and development.
Even the most basic flip-phones have more processing power than the most powerful graphing calculators. Why does a TI-83+ still take 10 seconds to draw a simple sine curve?
Obviously students should be taught, and asked to demonstrate an ability to perform all types of math without the aid of calculators. My Calculus II (Integrals) course in college allowed no calculators at all on tests.
The point is though, that when physics/engineering students need a tool to turn to for calculations, do we want their native “calculator language” to be a pencil, slide rule, graphing calculator, or matlab? I think engineers that were hacking matlab since middle school will be much more effective over the next generation than those who were using 20-30 year old hardware.
See: http://xkcd.com/768/
LOL – thanks Ross,
I take your point about the tools that students should be familiar with today if they are going to get serious about math and using it – I would add Mathematica to the list. At the same time, I think it’s important not to loose sight of the understanding and skills that underpin the effective use of these tools.
Long time viewer / first time poster. Really enjoy reading the blog, keep up the good work. Will most definitely start posting more in the near future.
Great blog, thanks. Been attempting to lose weight with the Cambridge diet these past couple of months and it’s going well. I will try and update soon to let you know how it’s going, so far I’ve lost 25 pounds in 5 months!
I am a Norwegian 17-years old girl. In my math class we are required to have a graphic calculator too, but the school offers us a free computer version to download if we don’t want to buy the expensive “real” ones. The TI-84 plus I bought was at a prize of about $400. We are requested to buy a Casio calculator, but the brand is not important as long as it has a graphic display. I bought the wrong one, TI-84 plus, and that is how I stumbled across this page, trying to figure out how it works, since my teacher only know how the Casio calculators work. Our school book explains both Texas’s and Casio’s procedures, but it’s kind of complicated. I do not know whether this is relevant, but I just thought it would be nice with some perspective from other countries 🙂
Hello, I’m currently taking the International Baccalaureate programme, and for my advanced maths class I was asked to purchase one of these 180 dollar geeks. I have not still bought it though they specified me tu buy that specific model. I will have to reflect it upon a little 🙁
My college statistics teacher is highly recommending the TI-84 graphing calculator, but I’ve found, personally, that Excel works much faster and easier if you’re able to use a computer. My classmates keep asking me to tutor them in Excel.
I see a lot of these calculators while substitute teaching in 5 middle schools and 2 high schools in two school districts. The focus in these districts on a particular make/model is based on two things: 1) the textbooks show opeations using these calculators and 2) if 30 kids had 30 different graphing calculators, the teacher would most likely be unable to answer calculator-specific questions regarding keystroke sequences. As a sub who has used a lot of calculators, including RPN calculators, I have to refer questions to other students because I am unfamiliar with the TI-83 and TI-84.
In postsecondary education, I went from programming computers in 1’s and 0’s, through assembly languages, to compiled languages. That route has led to a much better understanding of what is going on with the computer than modern “I have only seen object-oriented languages” provides.
In Physics class, we always had to be able to do the problem by hand before being allowed (and encouraged) to use calculators and computers to speed the redundant operations of calculation.
One of the biggest problems encountered in math and science classes it that the kids are now totally dependent on calculators – graphing or not. If the need to add a couple of 1-digit numbers arises, the first question out of the kids mouths is “can we use the calculators?” In this case, getting the calculator out will take longer than solving the problem by hand with pencil and paper (or, horrors! – doing the problem mentally).
So, make sure the kids can work the problem by hand, then, if the solution requires a lot of calculataion, let them use any tool that saves time.