Calculus without a calculator

[langfam]

Do any of your dc do Calculus without a calculator? DS did Chalkdust Calculus last year with a graphing calculator and did very well in the course. This past fall, DS's first semester in college he was advised to retake Calculus because they did it differently, so he was told. I was confused about it, but know now what they meant was they taught Calculus without using a calculator. He had to do everything by hand. Is this common for college math? He got a "B" in the class. I was wondering if the graphing calculator becomes a crutch and actually is harmful to real understanding. Just wondering for my other dc coming up who will be doing precal and maybe calculus in the future.

 

TIA

[LinRTX]

Two of mine have gone through Saxon Calculus at home. Both have gone on to college -- one in business, one in electrical engineering. It wasn't until differential equations that my son used a graphing calculator. That was after 3 semesters of calculus at college. We did use a scientific calculator, however.

 

Linda

[Brenda in MA]

My son used Saxon up through Advanced Math, and then we switched to Chalkdust for PreCalc & Calc. The use of the graphing calculator in PreCalc is what really, really helped him understand functions. He is very visual, and he learned so much more when he could quickly plug the function into the calculator to see what its graph looked like. That understanding carried in to Calculus as well for things like finding zeros, inflection points, etc.

 

In college this fall, I had him retake Calc I because I wanted to make sure he had it down well, and they don't allow calculator use on exams. He has been well prepared for that class having taken Chalkdust, and now he's sorry that he didn't take the Calc AB AP exam last spring to get out of Calc I at school. At the beginning of the term, he was pretty stressed about not being able to use the calculator on exams, but he managed to adjust, and already being familiar with the material helped as well.

 

I'm glad that he learned to use the graphing calculator because he also took a statics class this semester that required a lot of work with matrices. He had to show his work manually on exams, but they were allowed to use the calculator on exams, so he used it to check his answers. He was also allowed to use it to quickly solve many other types of problems. There is definitely a bit of a learning curve on using the graphing calculator, so I'm glad that he learned when he did.

 

For my ds, the graphing calculator aided his understanding rather than just being a crutch.

 

Brenda

[Julie of KY]

I made it through high school and college calculus as well as an engineering degree without anything but the basic calculator. In engineering if I really needed more than I could do by hand, I'd just write a computer program to solve it. In reality I understood everything better than my peers becuase I did it myself.

 

I have mixed feelings about using calculators in math today.

[Ruth in Canada]

I'm planning to do an introductory calculus course with dd next year. (We might end up doing the equivalent of calculus AP--but we also may go more slowly.) I really like the Thompson/Gardner "Calculus Made Easy" book for it's non-threatening explanations. I also have the calculus book I used 30 years ago. Neither (obviously) have any calculator use. How important is it that we use a graphing calculator? If most universities aren't allowing calculator use, then there's no point in me worrying about it. On the other hand, if dd will be expected to use a graphing calculator in a university-level calculator class, I may want to find another resource that expects graphing calculator use.

[Janice H]

 

I'd like to hear from more people about the calculators in calculus issue

Ruth, you could try this thread http://www.welltrainedmind.com/forums/showthread.php?t=127294&highlight=calculator

 

[Ruth in Canada]

Makes me wonder why there's so much emphasis on using graphing calculators at the high school level.

[Storm Bay]

Dr Stanley F. Schmidt, author of LOF, says that all you need is a scientific calculator for his Calculus class (that's in the beginning of the Trig book, since we don't have the Calc book yet.) Of course, he suggests using one of those for Algebra, too, but dd doesn't have one yet. She has used a regular calculator for doing irriational square roots, but that was after learning to do it without one, first. She says her answers are more accurate because the calculator rounds off too soon ;). I do want to get her a scientific one this year, though, for factorials and whatever else it is that it will help her with.

 

I think that Brenda made a great point, though, that learning styles come into play. It may be that one of my dc will need a graphing calculator to see it, but ideally not.

 

Of course, I still plan to make my kids learn to use dh's old slide rule because that's not a bad skill to have, either.

[Kendall]

I'm very interested in this. My son will complete Foerster PreCalc(required the graphing calc.) next week and is taking Calc I at the CC where a graphing calculator is required. I don't know about the 3 colleges that he is considering, but I'm going to check on that. When I called the local university they also said they require graphing calculators. The professor told me that some colleges don't allow them, but he gave me the impression that they were in the minority. I'm wondering if that is true.

[Janice H]

After understanding and learning how to graph (and in some cases it is an estimate) by hand, we use various online graphers for some types of problems. I like the online graphing programs because they are BIG, take very little time to learn how to use, and one doesn't have to fiddle on a different screen to change the zoom area. In this way we get to see the function relatively quickly and don't have to do everything by hand; it's a fast and clean way to make small changes to a function expression and see how it changes the graph.

 

Since we are also using CD precalc as a supplement, we have some idea of how the T-83 works when Dana M. uses it in the lesson. Incidentally the precalc dvd set can be ordered from the publisher for about $60.

 

Also, while dd will continue in math it doesn't look like she will be a science or math major, and for sure not an engineer. Obviously if you know your dc's college, major or profession uses graphing calculators you will want to do this differently.

[Amber in AUS]

Great discussion. We were taught to graph paper & pen style first and then using the graphics calc. However when it came to exams graphics calcs were allowed for math, but not for science. I think the use of a calculator too soon lead me to be lazy with my math and certainly i will be looking to hold off as long as possible and encourage a deeper understanding than i have even though i did well.

[Miss Marple]

Ds#1 was mentioning this the other day. He just finished Calc 3 at the university and has not been allowed to use a graphing calculator in any of his Calc courses. If the students wish, they can use a basic function calculator, but ds says that it is mainly to give the students a sense of security.

 

When I took calc in the dark ages, we didn't even have graphing calculators!

[asta]

So then which (home teachable) Calc programs actually teach calc w/o a calculator?

 

Kid is using MUS. It works well for him as he is extremely visual. Although he will need to "see" the graphs of Calc, DH and I both want him to be able to do Calc by hand. Will we need to supplement MUS with another program?

 

 

a

[Miss Marple]

So then which (home teachable) Calc programs actually teach calc w/o a calculator?

 

I have no idea. My boys do their higher maths at the local university as concurrent enrollment students. So their first exposure to calculus is at the university level.

[LoriM]

So then which (home teachable) Calc programs actually teach calc w/o a calculator?

 

 

a

 

Any older Calculus textbook (I personally like the Larson, Hostetler, Edwards books) will teach the student to draw their own graphs. I did Calculus at home with my daughter at age 15 for that very reason, so that she could learn to graph well. We never used a graphing calculator at home, and she bought her first calculator (and only calculator) when she entered College Algebra at 16. She used the Calculus with PreCalculus: A One Year Course for both PreCalc and Calc I, and I found it to be a very good book with clear explanations. It's designed to bring a student up algebraically, including graphing polynomial functions.

 

She was allowed calculator use through her entire math degree at the university, but never "taught" to use it.

 

Lori

[Storm Bay]

I have no idea. My boys do their higher maths at the local university as concurrent enrollment students. So their first exposure to calculus is at the university level.

 

 

LoF apparently teaches without a graphing calculator, because the author says you won't need more than a basic scientific calculator. But the older ones will teach it without one. Back in the electronic dark ages none of us had calculators until post high school, and prior to that you didn't even have them. You spent a great deal of money for what was basically a simple calculator by today's standards.

[Miss Marple]

A bit off topic, but I still have the HP scientific calculator I bought when I entered pharmacy school. We had to have something that figured logs and anti-logs. It is at least 25 years old and it still works. I never have to worry about the boys using it though, because of the strange way one entered data into the old HPs (I know there is a technical term for it, but can't remember it). I paid well over $100 for it then and can probably buy something comparable for under $50 now.

 

You spent a great deal of money for what was basically a simple calculator by today's standards.

Reply With Quote

[Dana]

I never have to worry about the boys using it though, because of the strange way one entered data into the old HPs (I know there is a technical term for it, but can't remember it).

 

Reverse Polish Notation - RPN

[asta]

LoF apparently teaches without a graphing calculator, because the author says you won't need more than a basic scientific calculator. But the older ones will teach it without one. Back in the electronic dark ages none of us had calculators until post high school, and prior to that you didn't even have them. You spent a great deal of money for what was basically a simple calculator by today's standards.

 

This is more what I was talking about.

 

I wouldn't be able to just pick up an old college text - I never made it past high school Trig, and I don't even remember it.

 

Kid and I are learning higher maths together. I wish we had the option of either an online course or a community college, but we don't. The time change is too great, and living in the middle of nowhere... eh.

 

 

a

[vonfirmath]

Do any of your dc do Calculus without a calculator? DS did Chalkdust Calculus last year with a graphing calculator and did very well in the course. This past fall, DS's first semester in college he was advised to retake Calculus because they did it differently, so he was told. I was confused about it, but know now what they meant was they taught Calculus without using a calculator. He had to do everything by hand. Is this common for college math? He got a "B" in the class. I was wondering if the graphing calculator becomes a crutch and actually is harmful to real understanding. Just wondering for my other dc coming up who will be doing precal and maybe calculus in the future.

 

TIA

 

I don't know about the answer to your question but I just discovered how early schools are required to have a graphing calculator and I'm disgruntled.

 

I went through AP Calculus BC, and passed the AP exam with a 5, without having ever used a graphing calculator. I went on to take 2 more years of engineering math without ever once needing this.

 

So I, too, am interested in teaching my kids the way to do math without the calculator (as well as how to use it just in case their college classes require it)

[Caroline]

The AP Calculus Exams, both AB and BC, currently have graphing calculator sections. There are problems that you would not be able to do in a timely manner without the use of the calculator. I am not saying that AP Calculus is the be all and end all of calculus instruction, just that you should plan for graphing calculator use if your child is going to take the exam.

 

I know Georgia Tech's graphing calculator policy in calculus depends on your professor. I know Professor Marley does allow students to use one, however there are other profs who will not let you use one.

[KnitWit]

My eldest only used Chalkdust up through Pre-Calculus. She just told me that Dana Mosley DOES teach how to work all the problems without a calculator, but then moves on to using the calculator. But, she said if one pays attention, it's there.

[In The Great White North]

Makes me wonder why there's so much emphasis on using graphing calculators at the high school level.

 

I think it's driven by the AP/College Board, both of which have written their tests assuming the students have a graphing calculator. Therefore, high school math teachers and texts have included graphing calculators so the students are familiar with them for the test. Some of them even go so far as to say "Enter this function. Zoom in on point (x,y)" so you can't really do the problem without one. Irritating to no end.

 

Could we get a list of colleges that teach calculus without the graphing calculator? I think it would be helpful to know which is more common.

 

Dartmouth doesn't allow them on tests.

[In The Great White North]

A bit off topic, but I still have the HP scientific calculator I bought when I entered pharmacy school. We had to have something that figured logs and anti-logs. It is at least 25 years old and it still works. I never have to worry about the boys using it though, because of the strange way one entered data into the old HPs (I know there is a technical term for it, but can't remember it). I paid well over $100 for it then and can probably buy something comparable for under $50 now.

 

 

Loved mine! Sadly, it went AWOL. Apparently, it has a fan club, trying to get HP to reissue it. At any rate, it goes for more now (ebay) than when I bought it new!

 

My dc hate RPN too. It's awesome for series and sequences!

[Halftime Hope]

Reverse Polish Notation - RPN

 

I was a chem major back in the mid '80s.

 

I did not know that the RPN designation was serious until today, as "polish" was often used in jokes, as in, "How many polish lab assistants does it take to...." I thought it was our funky physics prof's way of poking fun at the HP calculators. :lol:

 

(Students had both, but I ended up buying the TI.)

[emubird]

Using the graphing calculator for graphing functions is really a very useful pedagogical tool. It isn't a crutch. Having a graphing calculator will mean the student can get down to business with learning the material rather spending all their time trying to get their graphs to come out looking right.

 

However, graphing calculators also do a lot of basic calculus: derivatives and integrals. So a student could get away with never having to learn that "stuff" if they just plugged it into the calculator. This is probably why some college classes don't allow them on tests. However, they really are a useful tool for the graphing aspect of things, which is why a lot of colleges will require students to have them. (And a lot of the homework will need the graphing capability.)

 

The AP test now has several problems that really can't be done in a timely fashion without the graphing calculator. Some just can't be done at all without a computer or calculator. So a student really does need it for the test or they won't score as high. It's a different test than it used to be, so someone's experience on it years ago is irrelevant.

 

It does take more time to learn to use a graphing calculator than a scientific one. A student really ought to start using one in pre-calc, because they won't have time to learn it in Calculus if they're in a standard calc course. And if a student does a non-calculator calc course, they won't be at all prepared for the AP test.

 

However, knowing how to graph by hand is also a useful skill. Hopefully, a student will have learned this before they get to pre-calc.

[Elizabeth in WA]

However, knowing how to graph by hand is also a useful skill. Hopefully, a student will have learned this before they get to pre-calc.

 

Most standard calculus courses include curve sketching based on the first and second derivatives. You would need to learn this in calculus; it's for more complicated curves than those for which you could use the methods learned in algebra.

 

Does the AP test still include calculator and non calculator sections? Or is it all calculator allowed now?

[Kathy in Richmond]

Yes, the AP calculus exams (both multiple choice and free response questions) include both calculator-allowed and non-calculator sections.

 

~Kathy