When did you introduce/allow calculators for math?

[EKT]

My oldest is just finishing 8th grade, and we've never used calculators in math. We've used Math U See the whole way so far, and my kids have done great with the program, always doing all calculations in their heads (or using manipulatives, where applicable). My purpose in holding off on calculators was to make sure my kids' math facts and figuring were deeply learned and solidly established. I'd say my oldest has definitely achieved that goal!

Looking ahead to algebra I next year, I'm inclined to let my daughter start using a calculator for math. (At certain points throughout this past year, her current pre-algebra work has taken a very long time to complete each day. She is doing careful, accurate work, but I don't want math to become a grind she hates, so I'm inclined to let her use a calculator so she can work more quickly and efficiently.) 

I'm not a "math person," so I guess I'm just curious when others greenlit their children for calculators, and if there is any reason I should avoid them at this point? Again, I'm confident her math facts and understanding of math up to this point are solid. (I guess I'm just worried that calculator use might somehow weaken her established skills? Sort of like how now that I have a cell phone, I don't know anybody's phone number besides my husband and my sister, but when I was a teenager, I had dozens and dozens of my friends' and family members' phone numbers memorized....)

Would love others' thoughts and guidance. Thanks!

[Zoo Keeper]

They have to ask me before each lesson that they want the calculator and show me *why* they *need* the calculator.  Every time.  All the way through Alg 2, even.

I'm mean that way. 😉

Some things, like fussy stuff with square roots, or problems made for a graphing calculator-- that gets the green light.  Or some of the more soul-sucking piles of numbers that can show up in ugly pants consumer math type problems, punch those keys and get the answer and move on. 

But the "I just don't wanna do long division" moments?  Suck it up.  Do the math yourself.

 

 

[Not_a_Number]

In my experience, once you get to higher levels of math, you rarely need to do calculations that require a standard calculator. Plus, she's about to be exposed to a whole lot more functions whose properties she really SHOULD internalize without just pressing buttons... exponents, logarithms, trig, and so on, so forth. Honestly, it'd probably have been better to let her use a calculator in grade 7 and 8 than in algebra. 

I wouldn't hand her a calculator. 

[Arcadia]

For math, it was calculus BC. We bought the TI84 for that exam.
However my kids did use the Casio scientific calculator for high school physics and chemistry, as well as for SAT and ACT. 

[forty-two]

34 minutes ago, EKT said:

(I guess I'm just worried that calculator use might somehow weaken her established skills? Sort of like how now that I have a cell phone, I don't know anybody's phone number besides my husband and my sister, but when I was a teenager, I had dozens and dozens of my friends' and family members' phone numbers memorized....

I can say that this is very real.  I was an engineering major, and we joked about how we'd all lost our mental math skills because everything was either 2+2 or something insane - we had little practice with more-difficult-yet-still-reasonable numbers.  (It was embarrassing to play cribbage with my grandpa at 19 - I was so. stinking. slow. at adding that he'd end up just doing it for me, whereas in middle/high-school I could keep up fine.)  Also, in my high school honors math classes, people joked-with-too-much-truth about pulling out their calculators for anything more than 2+2 - and they did, too, and their calculation skills, both mental and pen & paper, declined accordingly.

My oldest is in 9th, doing Alg 1, and we don't use a calculator.  And honestly, ime in algebra there's really not much that requires one - everything's pretty straightforward with good number sense, and using a calculator too much disrupts the development of good number sense.  There's some apparently-hairy fraction calculations that can be done easily if you use some number sense to cancel things out, but if you just plug them into the calculator you'd miss it entirely.  And even in pre-algebra, for most of the calculations that took my dd a really long time, it wasn't because the numbers just sucked, but because she missed how they could play nicely if she did the problem differently. ETA: There was only one problem she had in middle school that really didn't deserve to be done by hand, but she'd already done most of it by the time I realized how annoying and pointless it was to calculate <oops>.

Like a pp, I'm more of a "calculator for a particular problem that deserves it", instead of allowing blanket calculator use.  If the numbers just don't play nicely no matter what you do - it's just going to be a nasty brute-force calculation - then by high school I'm fine with using a calculator for that.  But using a calculator regularly, on things that are kinda annoying but also can be simplified to an extent too - well, that's how you lose your number sense and your mental math skills.  Right now it doesn't occur to my dd to seek out a calculator - she expects to do things in her head and by hand - and I'm glad.  I watched my fellow honors students get calculator dependent really fast, and it took a lot of contrarian effort on my part to resist, to force myself to try to do things in my head and by hand before reaching for the calculator.  (And then of course I joined them in college, so embarrassing.)  My mental math skills are better now, after years of teaching elementary math (where I deliberately resisted using the answer key, but instead raced my kids to the answer), than they've been in years.

24 minutes ago, Zoo Keeper said:

They have to ask me before each lesson that they want the calculator and show me *why* they *need* the calculator.  Every time.  All the way through Alg 2, even.

I like that.

Edited May 18, 2021 by forty-two

[regentrude]

We never allowed calculators in math, all the way through calculus.

My kids used a scientific calculator for the numerical problems in chemistry and physics, and for the ACT (which is not about learning but speed).

Calculators in math detract from learning. Students need to develop number sense, see cancelations and simplifications, manipulate algebraic expressions, understand exponents, roots and logarithms without resorting to the crutch of plugging the numbers into a calculator. In many cases, using the calculator for these problems completely defeats the learning goal.

Edited May 18, 2021 by regentrude

[Dmmetler]

For test prep, because the ACT, at least, is designed to be done with a calculator and is next to impossible to complete in the time allowed without one. 

 

Some college classes so far have not allowed them, some have required them, and the same with outside science lab classes. My teen never used one at home for math because for AoPS, if you think you need a calculator, you're doing it wrong.  

[EKT]

I am so glad I asked! (I knew the math mamas would have good insight!) 

Okay, we will definitely continue doing math without a calculator (except for test prep and the upper-level math that specifically requires one). I will use other strategies (e.g., assigning fewer problems, etc.) if/when her math workload becomes truly punishing or unmanageable. 

Thank you for the help! 

[alisha]

I'm going to go against the flow here and say that there's a point when doing the basic operations by hand becomes busy work just to get the problem done. So, I let my kids use calculators as long as I KNOW they know how to do what they're using the calculator for without it AND it has nothing to do with the skill being taught.

So, for instance, if they're learning averaging and they KNOW how to add and divide, I think it's busywork to require them to do the problem without a calculator when what they really need to know is "add them all and divide by how many there are" not HOW to add and HOW to divide. As accountants, there's no way my husband or I would NOT use a calculator (or Excel) for the simple portions of complex, multi-step problems.

[Not_a_Number]

1 hour ago, alisha said:

I'm going to go against the flow here and say that there's a point when doing the basic operations by hand becomes busy work just to get the problem done. So, I let my kids use calculators as long as I KNOW they know how to do what they're using the calculator for without it AND it has nothing to do with the skill being taught.

So, for instance, if they're learning averaging and they KNOW how to add and divide, I think it's busywork to require them to do the problem without a calculator when what they really need to know is "add them all and divide by how many there are" not HOW to add and HOW to divide. As accountants, there's no way my husband or I would NOT use a calculator (or Excel) for the simple portions of complex, multi-step problems.

Yeah, that’s fair. That’s why I said calculators are reasonable for middle school.

But I wouldn’t use them for algebra. 

[daijobu]

MathCounts Target and Team Rounds assume the use of a calculator, so when they were prepping for MC I had them learn on an RPN calculator because of nerd cred.  Also, in AoPS Algebra you need to use a calculator for the chapter on interest rates. 

Apart from a few standardized tests, I don't think many people use calculators anymore.  You can google your calculations and graphs of interesting surfaces.

[NittanyJen]

12 hours ago, alisha said:

I'm going to go against the flow here and say that there's a point when doing the basic operations by hand becomes busy work just to get the problem done. So, I let my kids use calculators as long as I KNOW they know how to do what they're using the calculator for without it AND it has nothing to do with the skill being taught.

So, for instance, if they're learning averaging and they KNOW how to add and divide, I think it's busywork to require them to do the problem without a calculator when what they really need to know is "add them all and divide by how many there are" not HOW to add and HOW to divide. As accountants, there's no way my husband or I would NOT use a calculator (or Excel) for the simple portions of complex, multi-step problems.

Bingo. We are way beyond needing people to be human calculators any more, and requiring them to do the calculations by hand just slows things down so they can’t get on to doing more modeling and more interesting kinds of math that is more relevant today. Actual mathematicians do their math by computer, not by hand (I would know, I’m married to one, and ‘no calculator’ rules make him nuts).

 

[The Governess]

We have used calculators starting in Algebra 2:

1) When working with exponents and logarithms. At the very end of the unit I taught them how to use the different calculator functions. They were also allowed to use them on application problems like exponential growth and decay, future value of money problems, etc. 

2) When working with trig functions, after we had spent a lot of time working with special right triangles and exact values. 
 

3) At other times when solving applied word problems where the numbers would be cumbersome to work with and not using a calculator would detract from the skills I wanted them to focus on. Or where having a decimal approximation made more sense than leaving the answer in radical form, etc.

[regentrude]

7 hours ago, daijobu said:

Apart from a few standardized tests, I don't think many people use calculators anymore.  You can google your calculations 

Many of my college students are completely calculator dependent. They all use calculators in their homework and help sessions; heavily in chemistry and engineering classes. Googling calculations doesn't work in a classroom or lab.

[regentrude]

6 hours ago, NittanyJen said:

Bingo. We are way beyond needing people to be human calculators any more, and requiring them to do the calculations by hand just slows things down so they can’t get on to doing more modeling and more interesting kinds of math that is more relevant today. Actual mathematicians do their math by computer, not by hand (I would know, I’m married to one, and ‘no calculator’ rules make him nuts).

 

That argument makes no sense to me. It' s like saying we type and have spellchecker,  so students need not learn spelling. 

Just because a theoretical physicist uses a computer to solve complex integrals in their work doesn't mean a student no longer needs to learn integration techniques.

I see the fallout of lacking number sense. Math after algebra isn't about numerical calculations with lots of number crunching. The students who use calculators on their logarithms and exponent problems when they should simply using laws of exponents avoid learning what's at the core of the unit.

And that means they won't be able to do symbolic manipulations when there aren't numbers in the problems. 

[Farrar]

When the person who did the psych-ed testing on my kid told me I really had to. So... during geometry, which really doesn't make sense, but that just happens to be when we had it done. 

[Not_a_Number]

7 hours ago, NittanyJen said:

Bingo. We are way beyond needing people to be human calculators any more, and requiring them to do the calculations by hand just slows things down so they can’t get on to doing more modeling and more interesting kinds of math that is more relevant today. Actual mathematicians do their math by computer, not by hand (I would know, I’m married to one, and ‘no calculator’ rules make him nuts).

I'm an actual mathematician. As you can see, this is not something actual mathematicians are monolithic about... 

[Not_a_Number]

6 hours ago, lovelearnandlive said:

1) When working with exponents and logarithms. At the very end of the unit I taught them how to use the different calculator functions. They were also allowed to use them on application problems like exponential growth and decay, future value of money problems, etc. 

2) When working with trig functions, after we had spent a lot of time working with special right triangles and exact values. 

See, I wouldn't do either of those. I've taught trig something like 6 times now at AoPS and I can tell you that it often takes a few months before kids have a good intuition about how the trig functions behave, especially once you go outside the special right triangles. 

And most kids don't remember logarithm and exponent rules and can't use them fluently with numbers, never mind in algebraic expressions. 

Edited May 20, 2021 by Not_a_Number

[stripe]

6 hours ago, lovelearnandlive said:

We have used calculators starting in Algebra 2:

1) When working with exponents and logarithms.

 

I think my views are similar to yours.

In middle school, one of my kids did a lot from Mathematics: A Human Endeavor, which contains a great chapter on logarithms. At the same time, he became quite a fan of the slide rule my mom gave him, taught himself to use it, and therefore had two alternative calculating devices he could use, the other being the abacus.

Also, my grandpa did calculations when he was in the military and I’ve got his book of trig tables. These show up in HR Jacobs and other old textbooks. So I don’t think it’s ever really been expected that people have long square roots or trig values memorized.

I spent a lot of time on my kids’ mental math. I was also assigned giant arithmetic problems when I was in elementary school by uncreative teachers. I don’t care to have them do long arithmetic calculations by hand once they’re in high school. I also don’t believe in plugging everything into a calculator. I don’t find that they actually use a calculator that often. I have seen graphing calculators used as a substitute for basic understanding, and I would like to avoid that.

Edited May 20, 2021 by stripe

[Not_a_Number]

I think the bottom line on this discussion is that kids ought to be able to use calculators on everything they are already mentally proficient on and know all the properties of and would be able to estimate by hand if they HAD to. 

The problem is that I think a lot of people way underestimate how long this process takes for most kids. For example, many kids I knew in calculus were pretty shaky on FRACTIONS... 

[regentrude]

Another thing I observe: students who use calculators tend to uncritically believe in them and lack the skills to estimate whether the answer makes sense. I see that especially in calculations that involve scientific notation and exponents. They HAVE to estimate the order of magnitude using laws of exponents in order to detect when they made an input error. I had a student calculate the mass of Jupiter as 1.9 kg because she screwed up the exponents entering the numbers in her calculator  and was not used to always doing the order of magnitude estimate without the calculator. And that's not an isolated thing.  I have seen this over and over during my 20 years of teaching. 

[Not_a_Number]

25 minutes ago, regentrude said:

Another thing I observe: students who use calculators tend to uncritically believe in them and lack the skills to estimate whether the answer makes sense.

Yep. I see this all over the place. In exponents, in logarithms, in trig, even sometimes in division questions when we're trying to figure out when a rational function has an asymptote... 

[UmmIbrahim]

In reading these comments about having kids go beyond calculus without using calculators, I find myself wondering if the ability to do this isn't dependent on which curriculum is being used. My kids have done a lot of outsourced math classes, so I haven't been choosing the textbooks for the course (i.e. they are not the textbooks that I see great reviews for on these forums). In looking back at the way the problems were presented, there were many problems throughout Algebra I, Geometry, and Algebra II that seemed to be purposely designed with "gross numbers." 

I think the idea may have been to "get the kids used to" having all kinds of "real-world" decimals, radicals, etc. in the problems. If you've got decimals and radicals all over your problem and the directions instruct you to round your answer to the nearest hundredth, I really don't see how you are doing those problems efficiently without calculators. Sometimes the problems are designed so that you would be doing 3 or 4 long division operations in a single problem to arrive at a solution. Trying to get a kid through a curriculum designed like that without a calculator would seem, to me, to require more time spent in physical computation than actually working with the conceptual aspects.

Just a thought about math curricula in general and a perhaps a contributing factor to the differing feelings regarding calculator use.

[stripe]

Yes. I emphasize to my kids all the time the importance of using your brain first, with a calculator as a tool.

 I have the same conversation about GPS — there have been news articles about people blindingly following them and going all across Europe when they intended to go a short distance or whatever. 

[skimomma]

I am late to the discussion but I did not allow a calculator for math until dd took her first DE math course (pre-calc) at age 16 and it was required for that class.  Dd did have to use one for some of her science courses (outsourced) but even then, I only allowed a scientific calculator, not graphing.  I was warned by everyone that she would never catch up and be calculator proficient for standardized tests or college courses.  That has not been an issue.  At all.  Like others, I have two reasons for my philosophy.

As a college student (engineering), my class was the first to have a series of calc class option: Old school (plain old calculators), graphing calculator dependent, and math program dependent.  I had to take the old school style because I started in calc two and the options were only offered starting in calc one.  I lived this experiment.  In later classes, I knew my math MUCH better than the people tracked in the calculator and computer courses.  My dh and I are a closed experiment as he took the computer based path.  To this day, I can do mental math much faster than him and he actually blames our math paths from 25+ years ago.  That is pretty anecdotal and the fact that the classes were brand new could also be a factor.

After 13 years as a university instructor for freshman engineering students, I was flabbergasted that most of my students whipped out calculators when doing the most basic math.  Literally 2+2.  And their conceptual math skills were very weak.  As others mentioned, they have complete faith in what the calculator says.  No one seems to ask themselves, "is this number reasonable?" This was what really clinched it for me and even steered me towards and away from specific math curriculum....specifically high school math.  Even the most complex math can be introduced using numbers that do not require calculators.  

Dd caught up just fine with her peers when she needed to use a graphing calculator for DE math classes.  And she also transitioned to the computer programming methods that they use on her DE classes as well. 

Even if higher math was never going to be in the picture, having mental math skills is very handy for every day operations.

[forty-two]

1 hour ago, regentrude said:

Another thing I observe: students who use calculators tend to uncritically believe in them and lack the skills to estimate whether the answer makes sense.

Yeah, my engineering profs *hated* when people failed to notice that they'd forgotten to change their calculator from degrees to radians; they'd get something ridiculous like sin(Pi/2) = 0.03, but instead of realizing the problem and changing formats, they'd just blindly write it down.  I talk to my kids a lot about sanity checking their answers.

45 minutes ago, UmmIbrahim said:

In reading these comments about having kids go beyond calculus without using calculators, I find myself wondering if the ability to do this isn't dependent on which curriculum is being used. My kids have done a lot of outsourced math classes, so I haven't been choosing the textbooks for the course (i.e. they are not the textbooks that I see great reviews for on these forums). In looking back at the way the problems were presented, there were many problems throughout Algebra I, Geometry, and Algebra II that seemed to be purposely designed with "gross numbers." 

I think you're on to something here.  Our Pre-Algebra and Algebra texts are from the 60s, and expect everything to be done by hand, and so are designed that way - that all the calculations expected are pedagogically useful.  The one problem my dd did that really didn't deserve to be done by hand was from a state test (that did allow calculators, although it hadn't even occurred to me that it would till she hit that one problem) - it involved decimal multiplication and long division, and wasn't worth the effort to do by hand.  All they really wanted to test was the ability to know what to do with the (ugly) numbers. 

Edited May 20, 2021 by forty-two

[regentrude]

30 minutes ago, UmmIbrahim said:

In reading these comments about having kids go beyond calculus without using calculators, I find myself wondering if the ability to do this isn't dependent on which curriculum is being used. My kids have done a lot of outsourced math classes, so I haven't been choosing the textbooks for the course (i.e. they are not the textbooks that I see great reviews for on these forums). In looking back at the way the problems were presented, there were many problems throughout Algebra I, Geometry, and Algebra II that seemed to be purposely designed with "gross numbers." 

I think the idea may have been to "get the kids used to" having all kinds of "real-world" decimals, radicals, etc. in the problems. If you've got decimals and radicals all over your problem and the directions instruct you to round your answer to the nearest hundredth, I really don't see how you are doing those problems efficiently without calculators. Sometimes the problems are designed so that you would be doing 3 or 4 long division operations in a single problem to arrive at a solution. Trying to get a kid through a curriculum designed like that without a calculator would seem, to me, to require more time spent in physical computation than actually working with the conceptual aspects.

Yes, absolutely. That is why I prefer to use a well designed curriculum that focuses on the conceptual depth without wasting student's time on numerical computation that should have been mastered by 5th grade and are now mere busywork without learning. In Algebra and beyond, gross numbers obscure the objective. If a polynomial cannot be factored because the numbers are too ugly, students can't learn this part. If logarithmic problems are written so they can only be solved with a calculator,  students don't learn the principles of logarithmic laws. They learn efficient computation via button pushing, but not mathematics.

[regentrude]

3 minutes ago, skimomma said:

After 13 years as a university instructor for freshman engineering students, I was flabbergasted that most of my students whipped out calculators when doing the most basic math.  Literally 2+2.  And their conceptual math skills were very weak.  As others mentioned, they have complete faith in what the calculator says.  No one seems to ask themselves, "is this number reasonable?" This was what really clinched it for me and even steered me towards and away from specific math curriculum....specifically high school math.  Even the most complex math can be introduced using numbers that do not require calculators.  

Yep. I had college students reach for their calculators to multiply a number by TEN! Because they are soooo conditioned not to do any mental math. It's disturbing 

[Not_a_Number]

9 minutes ago, skimomma said:

No one seems to ask themselves, "is this number reasonable?"

I actually don’t think they know what being reasonable means. That requires robust mental models and they don’t have ‘em.

[UmmIbrahim]

15 minutes ago, regentrude said:

Yes, absolutely. That is why I prefer to use a well designed curriculum that focuses on the conceptual depth without wasting student's time on numerical computation that should have been mastered by 5th grade and are now mere busywork without learning. In Algebra and beyond, gross numbers obscure the objective. If a polynomial cannot be factored because the numbers are too ugly, students can't learn this part. If logarithmic problems are written so they can only be solved with a calculator,  students don't learn the principles of logarithmic laws. They learn efficient computation via button pushing, but not mathematics.

Yeah, I'm taking lots of these comments to heart and doing things differently with my youngest kid. He doesn't want to do outsourced math (live classes stress him out because he's a bit of a slower thinker), so I'm looking into the "older" curricula that seem to be better designed to teach concepts without gross numbers. When I looked at the Dolciani texts online, I realized that I had used Dolciani myself for Algebra II in high school back in the day!

My third son is a different kind of student who loves to think through things on his own (it probably comes from being the youngest and feeling more of a need to be independent). I'm currently figuring out which geometry text we'll be using next year, but I'm definitely leaning towards the older ones.

[skimomma]

4 minutes ago, Not_a_Number said:

I actually don’t think they know what being reasonable means. That requires robust mental models and they don’t have ‘em.

It hurts to watch.  I had one specific outcome that I tracked the entire 13 years.  One of the classes I taught involved drafting and scale.  Despite my having more teaching experience over the years, my students' ability to understand scale and therefore be able to recognize they had made a mistake declined significantly over the 13 years.  Between blind calculator faith and the fact that less and less of them had ever used a real map (hello GPS), more and more of them just could not grasp it as the years went on.  I had students turning in drawings of entire subdivisions on a sheet of standard engineering paper with a scale of 1:10.  There were all sorts of issues....not understanding how units worked, blindly following numbers punched into a calculator, or simply giving up and writing down something "official looking."  I would stand in the middle of the classroom with 10 sheets of paper lined up across the floor and ask the class if a subdivision would really fit in that space.  Blank stares.  

My first year, I had about 75% of the students leaving my class having eventually grasped the concept.  By year 13, I was down to about 40%.  I have no idea how to fix that once they are in college.  So many students asked why they needed to know this.  They told me that whatever CAD or solid modeling program they used would do this for them.  I kept pleading with them that yes, those programs do it for them but if they cannot assess what is reasonable, they cannot recognize mistakes.  You know, like BEFORE that bridge gets built or that airplane part is installed.  

[Not_a_Number]

2 minutes ago, skimomma said:

It hurts to watch.  I had one specific outcome that I tracked the entire 13 years.  One of the classes I taught involved drafting and scale.  Despite my having more teaching experience over the years, my students' ability to understand scale and therefore be able to recognize they had made a mistake declined significantly over the 13 years.  Between blind calculator faith and the fact that less and less of them had ever used a real map (hello GPS), more and more of them just could not grasp it as the years went on.  I had students turning in drawings of entire subdivisions on a sheet of standard engineering paper with a scale of 1:10.  There were all sorts of issues....not understanding how units worked, blindly following numbers punched into a calculator, or simply giving up and writing down something "official looking."  I would stand in the middle of the classroom with 10 sheets of paper lined up across the floor and ask the class if a subdivision would really fit in that space.  Blank stares.  

My first year, I had about 75% of the students leaving my class having eventually grasped the concept.  By year 13, I was down to about 40%.  I have no idea how to fix that once they are in college.  So many students asked why they needed to know this.  They told me that whatever CAD or solid modeling program they used would do this for them.  I kept pleading with them that yes, those programs do it for them but if they cannot assess what is reasonable, they cannot recognize mistakes.  You know, like BEFORE that bridge gets built or that airplane part is installed.  

That’s why I kind of prefer to work with young kids. Their sense hasn’t been knocked out of them.

To be fair, it turns out that mental models are genuinely hard to communicate. Most of us (me included) vastly underestimate how long it takes to get comfortable with an idea.

[lewelma]

My younger son *much* prefers to use trig tables over the calculator button. He feels like the calculator button is magic, a number pops out. It is just too easy to lose track of what you are doing and what it means.  The tables allow him to see the relationship between all the angles and ratios, and reminds him about going both ways in a way that a calculator never does. 

As for logs, I make him estimate the answer before he hits the button, even for base e.

I allow him to use a graphing package on the computer to graph most functions because he likes to explore what happens when you change different pieces of the equation. I feel like this improves intuition rather than reducing it because he is using a technological assist rather than graphing everything by hand. 

My older son is not allowed a calculator on any of his math or physics exams at University. And the numbers are not always nice. He told me that he does have to do a decent amount of long multiplication and division for certain physics exams. He is expected to be able to do it at speed (one time the professor gave the kids 20 extra minutes when he realized that the numbers were particularly messy, but still didn't allow a calculator).  My guess is that the profs care less about multiplication and division and more about having the intuition to deal with square roots, logs, and obviously fractions.  Take the calculators away and it forces kids to get fast and intuitive. They should be able to estimate first so they can confirm their answers make sense. Calculators undermine this intuition.

[lewelma]

For kids with Dyscalculia, I think that a calculator is a god send, and I would switch to it quite early. I have been able to teach a dyscalculia kid 12th grade statistics even though she could not subtract 9-6 at the age of 17 even with a tally chart. With a calculator she was empowered to do math, but if she had to do all the work by hand, she hated math and would make no progress, ever. I think switching her to a calculator at age 10 would have been a reasonable choice as she then would not have fallen behind. 

[Not_a_Number]

1 minute ago, lewelma said:

For kids with Dyscalculia, I think that a calculator is a god send, and I would switch to it quite early. I have been able to teach a dyscalculia kid 12th grade statistics even though she could not subtract 9-6 at the age of 17 even with a tally chart. With a calculator she was empowered to do math, but if she had to do all the work by hand, she hated math and would make no progress, ever. I think switching her to a calculator at age 10 would have been a reasonable choice as she then would not have fallen behind. 

Right. At some point, not teaching a kid who CAN'T have number sense how to use a calculator is like insisting a deaf person keep trying to "learn" to hear. It ain't going to happen. Now let's figure out how the person can function in the world... 

[SDMomof3]

We bought my ds a graphing calculator this year for his calculus class, but he has never used a calculator for his math classes before calculus. It’s good for them to workout the calculations. My dd had quite a few math classes at the university that don’t allow calculators. 

[lewelma]

I am currently working with a calculus student who wants to be an engineer, and am requiring him to estimate all angles in rad (not degrees) to make sure he gets intuitive with it. I also make him estimate sin/cos/tan ratios before hitting the button (and opposite direction). I'm getting him to memorize the early square roots, all the squares, cubes, etc.  I've told him that if he is building a bridge, he needs to be able to do some back of the envelop calculations while on site to get a feel for the problem.  He needs to have some of these numbers memorized.  He gets it.  This kid is particularly challenging because he failed Algebra 2 and trig last year due to poor teaching from Covid, but they have allowed him to move on to calculus. So we have a LOT of work to do. 

[lewelma]

2 minutes ago, Not_a_Number said:

Right. At some point, not teaching a kid who CAN'T have number sense how to use a calculator is like insisting a deaf person keep trying to "learn" to hear. It ain't going to happen. Now let's figure out how the person can function in the world... 

Agreed. There was NO WAY that she could ever learn basic calculations. But she could learn how to interpret statistical results.  This made her have a useful skill for the workplace as she was interested in political science and public policy. 

[Not_a_Number]

1 minute ago, lewelma said:

I am currently working with a calculus student who wants to be an engineer, and am requiring him to estimate all angles in rad (not degrees) to make sure he gets intuitive with it. I also make him estimate sin/cos/tan ratios before hitting the button (and opposite direction). I'm getting him to memorize the early square roots, all the squares, cubes, etc.  I've told him that if he is building a bridge, he needs to be able to do some back of the envelop calculations while on site to get a feel for the problem.  He needs to have some of these numbers memorized.  He gets it.  This kid is particularly challenging because he failed Algebra 2 and trig last year due to poor teaching from Covid, but they have allowed him to move on to calculus. So we have a LOT of work to do. 

Sounds potentially rewarding 🙂 . 

Unit circle alllll the way for trig, by the way 😄 . 

[lewelma]

Just now, Not_a_Number said:

Sounds potentially rewarding 🙂 . 

Unit circle alllll the way for trig, by the way 😄 . 

Yup. We review the unit circle EVERY DAY!  I make him explain to me the trig graphs in terms of the unit circle EVERY DAY.  We are doing calculus, but we are doing major revision of trig as he never even realized that it was about ratios. 

[Not_a_Number]

Just now, lewelma said:

Yup. We review the unit circle EVERY DAY!  I make him explain to me the trig graphs in terms of the unit circle EVERY DAY.  We are doing calculus, but we are doing major revision of trig as he never even realized that it was about ratios. 

I was the meanest person ever when I was tutoring my sister and made her graph all sorts of random weird functions that used trig BY HAND 😛 . She had to use the unit circle constantly. She had to estimate the square roots without a calculator. She had to find the point on the graph. She was super, super grumpy about it and thought it was the most boring thing ever.

... and she got through calculus at her competitive college with flying colors and is extremely grateful to me 😉 . 

There's really a lot to be said for doing things by hand. 

[stripe]

Do you have a suggestion for unit circle /trig practice?

[EKS]

I allowed a four function calculator starting in Algebra 1.  I also allowed a calculator for certain difficult word problems prior to that.

That said--calculators can do a whole lot of stuff now.  A whole lot of stuff.  The best thing you can do for your student is to make sure they can do by hand what would have been expected to be done by hand back in the day and also when and how to use the fancy calculator. 

[RootAnn]

There are at least a couple threads on this same topic if you search. Always the two camps (plus a few in the middle). I'm on team No Calculator [until you need it for whatever class].

I agree on what @UmmIbrahim said about outside classes & textbooks.

I try to get that number sense into my kids. They accuse me of making them do the problem twice when we estimate the answer first. I tell them it is easier than redoing the problem when their answer isn't close (decimals wrong, multiplied instead of dividing, etc). Plus, it helps them to actually think through what they need to do in story problems. 

My dd#1 is a math major. No calculators in Calculus & other "lower level" math courses. Some kids who got As in AP Calc fail their first semester Calc class (retaking for an easy A) because they can't handle the math without the calculator.

[Not_a_Number]

1 hour ago, stripe said:

Do you have a suggestion for unit circle /trig practice?

Really, if you use the unit circle every single time you see a trig function, it should be very useful. I have other tricks I use, but just making sure that a kid USES the unit circle is halfway there. 

[lewelma]

6 minutes ago, Not_a_Number said:

Really, if you use the unit circle every single time you see a trig function, it should be very useful. I have other tricks I use, but just making sure that a kid USES the unit circle is halfway there. 

Agreed. I just require that they draw the unit circle and interpret the question in terms of it for every question they do.

[lewelma]

Basically, just use it until it is second nature, and then you just use it at that point because it is second nature!

[Not_a_Number]

Just now, lewelma said:

Agreed. I just require that they draw the unit circle and interpret the question in terms of it for every question they do.

Right. It was a lot trickier to come up with questions that MADE kids pull up the unit circle from their memory for my precalc class, since I wasn't going to be there when they did the problem. But if I'm monitoring the work, it's pretty easy. 

[EKS]

38 minutes ago, Not_a_Number said:

Really, if you use the unit circle every single time you see a trig function, it should be very useful.

I literally draw a pair of axes and a circle every time I have to do certain trig things, even if all I do is stare at it while thinking.

[daijobu]

6 hours ago, Not_a_Number said:

I was the meanest person ever when I was tutoring my sister and made her graph all sorts of random weird functions that used trig BY HAND 😛 . She had to use the unit circle constantly. She had to estimate the square roots without a calculator. She had to find the point on the graph. She was super, super grumpy about it and thought it was the most boring thing ever.

... and she got through calculus at her competitive college with flying colors and is extremely grateful to me 😉 . 

There's really a lot to be said for doing things by hand. 

Grumpy?  This was high school for me.  We drew little daisies and funny curves using polar coordinates [r,theta] by hand.  It's slow and tedious but I feel that plotting the various equations slowly and carefully also gave me time to think about what is going on.  We also did this with regular old linear equations, hyperbolas, sine functions and hyperbolic paraboloids.  We drew torii, parabolas that were rotated in 3D on their axis, spheres inscribed in cubes, math was often an art class.  By hand, pencil and paper, no calculators.  (Graphing calculators had only recent become available, and few people owned one.) 

I can still draw a hyperbolic paraboloid (saddle for a 2 hump camel) by hand for you in 30 seconds.