When to start using a calculator?

[Jenmomof3]

I'm curious when you start allowing the use of a calculator in math? My ds started AOPS pre-algebra this year and it is taking quite a while to complete the problems. I know they're supposed to take some time, but I'm wondering if we're at the stage where I should allow him to focus more on the problem solving and less on the mechanics by letting him use a calculator. Up to now, I've been very opposed to calculator use, since I wanted him to continue to strengthen his mental math. Now I'm wondering if we've arrived at the level where it's time to reconsider. Thoughts? What do you do?

 

Thanks!

[regentrude]

Can you give me an idea for what kind of problem you feel that using the calculator would be beneficial?

 

In AoPS, the problems are almost always supposed to be worked without a calculator. There is hardly any tedious arithmetic; all the problems are designed so that a calculator is unnecessary. Very often, using the calculator in AoPS would make a problem completely miss its goal: for example, problems about laws of exponents (one area where many people feel the student should use a calculator) are designed so the student uses the laws to simplify his calculation to such a degree that the answer can be obtained very easily.

ETA: you're supposed to leave things like sqrt(2) and pi as they are; much more accurate and concise than substituting a numerical value.

 

We are using AoPS, and have not really needed a calculator all the way through precalculus. Even the AoPS trig problems are such that simple answers can be obtained by thinking. We don't need one now in AoPS calculus either (we will introduce a graphing calculator soon because the AP test has problems that can not be solved without, which I find utterly stupid)

I allow a calculator for computations in physics and chemistry.

 

ETA: There are other curricula which are less well designed and where a calculator is needed earlier. But usually not before the student needs to compute values of trigonometric functions, logarithms, and exponentials.

Edited September 14, 2012 by regentrude

[Jenmomof3]

Thanks for the reply regentrude.

 

You're right. Now that I'm thinking about it more closely, most of the problems are about simplifying the equations. He is really doing well with that, so maybe the calculator is not the right solution.

 

I think the problems I was mostly thinking about using a calculator on were those that you narrow down the range, but then have to do trial and error to narrow down the range further (i.e. N is an integer such that N cubed equals 4913). He's great about knowing it's between 10 and 20, but then you try 15 cubed, too low, then he might try 16 cubed, still to low, etc. - not a huge amount of calculation, but it still takes time.

 

I guess maybe I'm really just trying to find a way to make the process quicker as I can't see how we can get through this book in a year at the rate we're going (although he's younger, so I guess I probably shouldn't worry about us taking longer, maybe I just need to adjust my expectations). I have allowed him to skip the challenge exercises since he's also sitting in on our Mathcounts team meetings. I'm not sure if that's a good decision or not - do you have any insight on whether the challenge exercises are necessary?

 

It's so nice to hear that you went all the way through Calculus without using a calculator, as I am really not a calculator fan. I guess we will just stay the course and see if things pick up as he gets more familiar with this method. All in all, he is really loving this curriculum and learning a lot.

 

Thanks again.

[Halcyon]

I just began allowing my son to use a calculator for SOME CWP problems, assuming he has already written out all the work, and just needs to the calculator for multidigit multiplication or something. He knows he is not allowed to use it for anything he can do in his head, and must show all his work. The reason I am allowing it is because he will be taking Explore in January and he needs to know how to use a calculator for the exam.

 

He does not use it for AoPS, but we are only beginning Chapter 2, so I am not an expert.

[regentrude]

I think the problems I was mostly thinking about using a calculator on were those that you narrow down the range, but then have to do trial and error to narrow down the range further (i.e. N is an integer such that N cubed equals 4913). He's great about knowing it's between 10 and 20, but then you try 15 cubed, too low, then he might try 16 cubed, still to low, etc. - not a huge amount of calculation, but it still takes time.

.

 

Ah, but on a problem like this, you can progress further with some more thinking instead of trying:

4913 can not possibly be 15 cubed, because 15 cubed has to end in a digit 5.

It also can not possibly be the cube of an even number, because 4913 is odd, so 12, 14, 16 and 18 are out.

This way, he should try to eliminate more possibilities before trying out the calculation. Using the calculator makes the trying out too easy, and the student might not try hard enough to get by with just thinking. If you are using AoPS, it is very likely that trying out will be minimal and that there are shortcuts he has not been seeing.

[Crimson Wife]

I plan to start allowing calculator use at Algebra 2. That is when my high school started requiring a graphing calculator.

[Jenmomof3]

Good point regentrude.

 

Thanks for the replies Halcyon and Crimson Wife.

 

I may be more open to using the calculator at some point in the future, but I think for now we'll stick with our paper and brains and hope we speed up as we learn more.

 

Thanks again for helping me think this through!

[boscopup]

I'm halfway through chapter 4 of Prealgebra myself and haven't felt like I needed a calculator for anything, despite having mommy brain and not doing a ton of mental math over the years (I use my computer calculator a LOT). As regentrude said, usually you're supposed to use what you've learned to simplify the problem. If you find yourself having to make huge calculations, you probably need to stop and redo it a different way. ;)

[jennynd]

I allowed my son to use on average/mean, area of circle when it involve pi , we are in algebra now and do not feel have a need to use calculator for a while

[Julie of KY]

I would not allow a calculator for AoPS prealgebra. The book is designed to be done without a calculator. If you read the solutions, you can learn how the problems can be done without the calculator.

 

Don't worry if you take it slow and steady through the book. It's not a race and the understanding of math will be so much deeper if allowed to process and internalize the concepts.

[Grantmom]

Ah, but on a problem like this, you can progress further with some more thinking instead of trying:

4913 can not possibly be 15 cubed, because 15 cubed has to end in a digit 5.

It also can not possibly be the cube of an even number, because 4913 is odd, so 12, 14, 16 and 18 are out.

This way, he should try to eliminate more possibilities before trying out the calculation. Using the calculator makes the trying out too easy, and the student might not try hard enough to get by with just thinking. If you are using AoPS, it is very likely that trying out will be minimal and that there are shortcuts he has not been seeing.

 

Yikes, see now this scares me, because how will I/he know these kinds of tips? I would have totally done the trial and error thing too. Does it explain these additional things to you in the teacher's manual or something?

[boscopup]

Yikes, see now this scares me, because how will I/he know these kinds of tips? I would have totally done the trial and error thing too. Does it explain these additional things to you in the teacher's manual or something?

 

The text teaches the student. AoPS works like this: You do the "problems" first. These are worked again with full solutions on the next page. Usually, the problems aren't that hard, but they are teaching an important concept that you will need to know in the "exercises" section. It has a very full explanation, as if a teacher is talking. AoPS has a lot of words, since it's self-teaching. Once you do the problems and go over the text, you then do the "exercises". These take the concepts learned and apply them in different ways. You have to think! After all, they are teaching the child to "problem solve". All the tools are provided. It's up to the child to figure out how to use them. The child is not spoonfed with "for this type of problem, do xyz". The child is instead taught the properties, laws, etc. that they can use in math in general, and they learn how to apply those to a new problem they've never seen before.

 

The solutions manual has full solutions, so if you are completely stumped, you can go there and find out how to do it. Some problems also have hints in the back of the student text that you can use before resorting to the solutions manual.

 

If you use the online component, Alcumus, those problems also have full solutions. :)

[regentrude]

Yikes, see now this scares me, because how will I/he know these kinds of tips? I would have totally done the trial and error thing too. Does it explain these additional things to you in the teacher's manual or something?

 

there is no teachers manual. The text is written to the student. All solutions to the problems are explained and discussed in detail in the text, and the solution manual has fully worked solutions for all problems.

 

Don't worry if you don't see the short cuts at first; working all the problems and thinking about them will teach the problem solving. As boscopup explained, this is not about memorizing and drilling a procedure for every particular type of problem, but about developing thinking skills.

I would recommend that you carefully study the solution to every problem even if you did find out the answer yourself. Often, you'll discover that there would have been more elegant and efficient ways to do it, and from that you learn.

Edited September 15, 2012 by regentrude

[Poke Salad Annie]

Ah, but on a problem like this, you can progress further with some more thinking instead of trying:

4913 can not possibly be 15 cubed, because 15 cubed has to end in a digit 5.

It also can not possibly be the cube of an even number, because 4913 is odd, so 12, 14, 16 and 18 are out.

This way, he should try to eliminate more possibilities before trying out the calculation. Using the calculator makes the trying out too easy, and the student might not try hard enough to get by with just thinking. If you are using AoPS, it is very likely that trying out will be minimal and that there are shortcuts he has not been seeing.

 

:iagree:

 

This is the kind of skill we were working on yesterday, though we are not using AOPS. (I'm glad to know that I'm on the right track with some of the bits and pieces I've put together.)

 

What I'm trying to instill at this point is the building of skills, much like what regentrude has described. To me, this is where logical thinking comes in, and I try to stress that daily.

 

I don't allow calculators here, at least until much later. (I'm not even sure if anyone is aware that there is one in the house. ;))

Edited September 15, 2012 by Poke Salad Annie

[Beth in SW WA]

 

I let dd use a calculator in cwp 5. She doesn't use one in algebra...yet. :) KB Alg 1 teaches how to use a graphing calc. Dd will think that's fun.

[Grantmom]

I understand it's not spoonfed, and not about memorizing, drilling, etc, that's definitely what I'm drawn to about it. I just mean, that example above, I just don't know that I would have ever figured that out on my own, if they don't give you that tip at some point. Like the other poster who said they were just doing trial and error and it was getting tedious, that would be what I would have done too.

 

I guess we'll just have to get it and try it out and see if it's a good fit. Thanks!

[Sebastian (a lady)]

The Intro to Algebra book contains both algebra I and algebra II material.

I think chapter 13 is a common goal for the first year. We got to chapter 11 and then spent the summer doing polynomials in a Dolciani book until they had mastered the ideas.

 

Now we're moving at a better pace as we do algebra II.

[Sebastian (a lady)]

The biggest change we had to make was to actually try to solve the sample problems even/especially when they seemed obvious. That is were you are forming the understanding of the concepts.

 

In lower grades with Saxon the samples seemed just like examples to glance at and then refer back to if you got stuck. They were probably intended to be used simarly but aops really requires it, in our experience.

[boscopup]

I understand it's not spoonfed, and not about memorizing, drilling, etc, that's definitely what I'm drawn to about it. I just mean, that example above, I just don't know that I would have ever figured that out on my own, if they don't give you that tip at some point. Like the other poster who said they were just doing trial and error and it was getting tedious, that would be what I would have done too.

 

 

You probably wouldn't, once you've gone through the problems in that section and learned the concepts. Then you get to the execises and are looking for ways to use what you've just learned. That problem pops up, and you think, "Aha! I learned xyz in the problems, and that applies here!" :D

 

It will take some getting used to, but pretty soon, you realize that if you're making the problem too complicated, you need to redo it. ;) At least in the prealgebra book, all of the problems have been relatively simple to work IF you apply concepts. I'm only halfway through chapter 4, but that's how it has been so far. In fact, I learned from AoPS how EASY LCM and GCF were to solve if you just find the prime factorization of each number, and I taught it to my son when he hit those topics in Singapore 5A. Way easier than what I was taught, and I've remembered it because I fully understood "why" it works. In fact, if I forget which way to do it, I just look at the prime factorizations and can work it out again what to do because it makes sense. In school, we just listed the multiples of each or the factors of each until we found what we were looking for. That's so inefficient!

[Grantmom]

Thanks, all! I am excited to get it now. I may go ahead and get it now and begin to work through it on my own so I start to understand better too. Thank you for this discussion.

[Woodland Mist Academy]

We used some of Aops pre a and for sure you wouldn't want to use a calculator with that.

 

:iagree:You would be missing the point.