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The math department in the ps where I work is really fragmented and at polar opposite points right now (sigh).  There are those who insist on teaching things SOLELY via calculator and those who want to teach MATH.  (Yes, I'm in the latter group.)

 

I was just giving a test for one of the Alg teachers who's a calculator person... it was horrid.  The kids are completely unable to think about anything deviating from the basic - and then they have to remember when to use what, etc.

 

So many kids were asking questions about the test - not understanding what was being asked of them.  I'll admit to explaining some of the questions for them (not giving answers - just putting the questions into other words for them), but it was frustrating as I know doing so will make the stats look better for this teacher.

 

I know these kids.  I like these kids.  I feel for them - hence the vent.

 

And I'm so glad I chose to homeschool my own.  I still wish youngest had opted to homeschool his high school years too.

 

Right now I'm feeling a wee bit selfish at not going full time, but on the other hand, if I did, I would have to adhere to school policy and have tons of paperwork, etc.  I wouldn't have the same freedom I do now.  Going full time is not the least bit appealing other than to help the kids out.

 

I really prefer when I'm NOT in for testing days.

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That sounds so frustrating. I'm glad you're there doing what you can.

 

It gets really bad on days like yesterday when I was in for learning support.  Learning support still teaches the whys and hows of doing things - it really does help the kids understand IMO (and theirs).  But several of them have teachers who are calculator-only folks.

 

So, on the one hand, we're working with them trying to teach them methods to solve quadratic equations and the teacher is telling them to skip all that and just find the zeros from the graphing calculator.

 

The poor kids are caught in the middle thinking we're all crazy - and it's not like they want to learn algebra anyway.

 

It's the kids I really feel sorry for.  I can agree that these kids don't need algebra, but since the state says they do... it's an UGH situation.

 

Testing-wise they seem to me to do better with background than just being taught the calculator, but maybe I'm biased.

 

I had one yesterday graphing an absolute value equation upside down - not due to incorrect calculator usage, but due to an idiot who messed up his calculator.  I had to totally clear the memory to get it to graph correctly.  The young lad had no idea it was wrong - even a simple error like being upside down.  Learning support kids can usually "get" the simple things like that IF they are taught them.

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My daughter lost major math skills the one year she was in public school (9th grade) because of the overuse of calculators.  They were instructed to use calculators to add and subtract for goodness sake!  The thinking is calculators will always be available and by using it for simple math they didn't have the problem of stupid simply math errors messing up their answer.  I do quick math in my head all the time.  Stuff like my distance to empty on my van is x, it's y far to where I'm going, do I need to get gas now or can it wait, adding up about how much stuff will cost at a store, etc.  My daughter and her classmates are so dependent on calculators, that sort of thing either takes much longer than it should in their head or they have to whip out a calculator to do it.  It drove me absolutely crazy.

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OK, I'm old, but I was doing through multivariable calculus without a calculator. I'm really against the use of the calculator in any high school math. It seems all the major publishers introduce calculators in 3rd grade now, so no one has to master even basic arithmetic. Students do not have any idea what is happening to numbers when they multiply. Forget fractions, decimals and percents. My dc went to/go to public high school, but I taught them math into algebra 2 before they went.

 

I teach in a program that serves public school students. None of these students have any idea what to do with a fraction. It's just awful.

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I've had kids in Alg 2 classes not be able to do 4x100 in their heads.  It's really sad IMO.

 

What I don't understand is why these teachers became MATH teachers when all they want to do is teach calculator usage.  It is mainly the younger generation to be honest.  We old fogies are being phased out.

 

One could perhaps go along with the "need calculators" for learning support, but these teachers/classes do not only have learning support kids in them.  Some of these kids want to go to upper level schools.  What happens when they get there and aren't allowed to use calculators in their Calc classes (middle son couldn't)?  He said several of his classmates were quite dismayed, so it isn't coming just from our school.

 

We're told "top kids are smart enough to catch on if/when they need it."  Perhaps so, but perhaps they can do better if we TEACH it in school IMO.  Isn't that what school and MATH classes are for?

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One could perhaps go along with the "need calculators" for learning support, but these teachers/classes do not only have learning support kids in them.  Some of these kids want to go to upper level schools.  What happens when they get there and aren't allowed to use calculators in their Calc classes (middle son couldn't)?  He said several of his classmates were quite dismayed, so it isn't coming just from our school.

 

I see that all the time in physics. Students are calculator dependent and can't divide or add fractions. They are not permitted to use a calculator in engineering physics 1, all problems are in symbols - but there may be simple factors and fractions even when it's a purely algebraic problem. Forget about knowing basic trig without a calculator...

 

 

 

We're told "top kids are smart enough to catch on if/when they need it."  Perhaps so, but perhaps they can do better if we TEACH it in school IMO.  Isn't that what school and MATH classes are for?

 

This, and they will not fully develop their math skills if they have been hooked on calculators for 10 years and did not get a chance to develop their feeling for numbers over the course of a decade. They will never learn to "see" squares and factors and cubes and primes the way a student who does all his math without calculator through high school will.

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This, and they will not fully develop their math skills if they have been hooked on calculators for 10 years and did not get a chance to develop their feeling for numbers over the course of a decade. They will never learn to "see" squares and factors and cubes and primes the way a student who does all his math without calculator through high school will.

 

They do not get the slightest feel for when their calculator might be wrong due to operator error or otherwise.

 

They could be adding 4+5+7 and get 356 (somehow) and see nothing wrong with it.  Ditto that with thinking 400 could be 10% of 40 if they forget to push the % button.

 

They can be graphing lines and totally not get that they missed a negative when they see an increasing line, but the problem had a negative slope.

 

They can square -7 and argue with me that it HAS to be -49 as that's what their calculator is telling them.

 

There are just far too many foundational basics that they are missing IMO.

 

Sometimes I'll admit to wondering if the (calculator-loving) teachers themselves know these foundational basics or not.  I think they do - honestly - but how do they not see that (too much) calculator usage is not passing that knowledge on?

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They do not get the slightest feel for when their calculator might be wrong due to operator error or otherwise.

 

They could be adding 4+5+7 and get 356 (somehow) and see nothing wrong with it.  Ditto that with thinking 400 could be 10% of 40 if they forget to push the % button.

 

They can be graphing lines and totally not get that they missed a negative when they see an increasing line, but the problem had a negative slope.

 

They can square -7 and argue with me that it HAS to be -49 as that's what their calculator is telling them.

 

There are just far too many foundational basics that they are missing IMO.

 

Sometimes I'll admit to wondering if the (calculator-loving) teachers themselves know these foundational basics or not.  I think they do - honestly - but how do they not see that (too much) calculator usage is not passing that knowledge on?

 

If they had learned properly themselves and internalized the concepts, they'd be more likely to argue that the students can do the same instead of insisting that they can't. They'd be adamant about it, knowing how hamstrung the students would be with a push button math education.

 

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They do not get the slightest feel for when their calculator might be wrong due to operator error or otherwise.

 

They could be adding 4+5+7 and get 356 (somehow) and see nothing wrong with it.  Ditto that with thinking 400 could be 10% of 40 if they forget to push the % button.

 

They can be graphing lines and totally not get that they missed a negative when they see an increasing line, but the problem had a negative slope.

 

They can square -7 and argue with me that it HAS to be -49 as that's what their calculator is telling them.

 

There are just far too many foundational basics that they are missing IMO.

 

Sometimes I'll admit to wondering if the (calculator-loving) teachers themselves know these foundational basics or not.  I think they do - honestly - but how do they not see that (too much) calculator usage is not passing that knowledge on?

 

This is a really serious problem.

 

If someone computes the mean of ... let's say ... 10 double-digit numbers, and the correct answer is 45, and they get 43, ok, I can see that.

 

If they get 443, I can't see how you could possibly not realize that's wrong. 

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This is a really serious problem.

 

If someone computes the mean of ... let's say ... 10 double-digit numbers, and the correct answer is 45, and they get 43, ok, I can see that.

 

If they get 443, I can't see how you could possibly not realize that's wrong. 

 

And this is exactly what is happening.  If their calculator showed 443, well then, 443 MUST be the answer.   There is no in-depth sense that something must be wrong with their calculation. 

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And this is exactly what is happening.  If their calculator showed 443, well then, 443 MUST be the answer.   There is no in-depth sense that something must be wrong with their calculation. 

 

Yes.

 

I have a policy in my classes that answers that defy common sense will not receive partial credit, no matter how much of the problem is correct.

 

For example: If I tell you a bank account of $1500 is invested at 3% interest, and ask how much is in it after 5 years, any answers LESS than $1500 receive an automatic 0. 

 

Quite honestly I've thought about awarding negative points for those (just to emphasize that sometimes it is more important to say "I have no idea" than to say something that you know is wrong), but I have not yet gone that far. 

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Sometimes I'll admit to wondering if the (calculator-loving) teachers themselves know these foundational basics or not.  I think they do - honestly - but how do they not see that (too much) calculator usage is not passing that knowledge on?

 

They probably don't have the foundational basics themselves, or they'd know they are important. A slightly more generous view is that they were taught the same way but have a natural intuition for math and think others can figure out the same concepts as they did.

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creekland, I do not envy you your situation.  That is a tough place to be, and honestly by that level it is going to be really hard to go back and fix what is really a problem that starts in Elementary, IMHO.   :grouphug:

 

I have a child that has always struggled mightily with math.  It will probably never be an easy subject for her.  She has been climbing this nearly impossible uphill battle with math for years.  Some told me once I started homeschooling for 6th grade that it was a lost cause, that she should just be handed a calculator and taught life skills math.  I didn't want to give up on her.  I started her over with basic subitization skills.  We went slow.  We worked on comprehension of the numbers.  It is working.  She needed way more detailed, explicit instruction and way more practice to mastery, as well as constant review of previous skills than she ever got in brick and mortar, but as a homeschooler I can give her that.  I just wish we had started years before we did.  

 

But many of her classmates that found math far easier that she did are now struggling in higher maths since they were not given the time/instruction to understand and master math at the lower levels.  They were able to rote memorize some algorithms and move forward without any understanding.  Handing them a calculator doesn't fix that issue, it exacerbates it.

 

 I am not a whiz at math.  I have to really think hard to understand and process what I am doing.  Years and years of just using a calculator made the situation much worse.  It wasn't until I was having to go back and relearn the basics, not through rote memorization (which is how I was taught) but through a combination of conceptual understanding and constant exposure to the patterns, that I actually started to understand math.  And you know what?  Math is actually very interesting, and can be quite fun.  Getting some deeper understanding made higher math more interesting and even possible, which in turn is giving me the chance, for the first time in my life, to be able to think through something, recognize when numbers are off no matter what the calculator says, etc., and hopefully teach my daughter, too, even if it takes us many years to get there.

 

But so many kids who might find math easier than DD and might really enjoy it and do exceedingly well in higher math are going to never gain any understanding because they are rushed through the material too early in elementary, and then are handed a calculator way too early before anything is truly mastered or internalized.   The foundation is never established.  Then the High School teachers are frequently blamed.  They may or may not compound the problem, but the issue begins long before High School.  Many kids are being crippled, slowly, over years.  And that just saddens me...

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I don't know.  I have multiple opinions about calculators and they don't agree.  :)

 

Not counting learning disabilities:

1) I think you should learn the problem first without a calculator.

2) I think addition and multiplication facts should be mostly memorized.  With fact families they can figure out the subtraction and division.

3) There is a point where calculating 97^24 is a good problem for a calculator.

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I don't know.  I have multiple opinions about calculators and they don't agree.   :)

 

Not counting learning disabilities:

1) I think you should learn the problem first without a calculator.

2) I think addition and multiplication facts should be mostly memorized.  With fact families they can figure out the subtraction and division.

3) There is a point where calculating 97^24 is a good problem for a calculator.

I agree (for clarification, though, since I am not clear on your position here, I don't think heavy emphasis on rote memorization instead of number sense is a good idea for most kids; I think both, when possible, are really important).  And I get a bit conflicted about calculators and when they should be used.   :)

 

If I didn't have a calculator, I would really hope I could do a significant amount of math without it.   Calculators in and of themselves are not evil, though, and can be an extremely useful tool.  I just really, really disagree with teaching a child dependence on calculators before there is any real understanding of the underlying math.  And I am a parent that struggled with math and have a child with learning challenges that make math quite hard.  A calculator would be an easy crutch to grab every time we do math.  It would also be a limiting one, KWIM?  So I am still working through when a calculator will become part of our lives.

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Oh gosh, for most kids I agree on the calculator stuff, but for dd15 who has some kind of undiagnosed not-quite-dyscalculia, they are the world's greatest blessing. The calculator lets her feel more confident. She feels good about being able to use the calculator. Without a calculator she would drown. As it is, she only just has her nose above water.

 

But yeah, that's not most kids. Ds isn't allowed near one.

:grouphug:  :grouphug:  :grouphug:

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I am all for calculators in their time and place.  They can make difficult problems far more easy to do IRL.  Weird functions can be easily graphed and differentiated.  Complex calculations can be done at our fingertips quickly.  I don't feel we need to go back to the stone age.  I just think kids should learn MATH first.

 

I think kids should actually understand addition, subtraction (negatives essentially meaning a change in direction), multiplication, and division.

 

I think kids should grasp fractions and how they work with all of those functions to the point of being able to explain them.

 

I think they should grasp that square roots are the sides of squares with that area, that exponentials are a way for compounding or depreciating things (and what that means), that division by zero doesn't make sense, and what inequalities mean.  I want them to look at graphs and comprehend them - being able to explain them.

 

Whatever they are doing, I want kids to be able to explain it to me what it means in basic English.  It's how I ALWAYS start my class since I'm coming in subbing and need to see where they are.  It's rare that they can do this, so I start there - many times even having to back up because they missed foundational things.  But I can't do this on testing days.

 

On today's test they were given two points and had to create a line in three forms - y intercept, point slope, and standard.  Way too many kids got the first (if they didn't make a stupid mistake calculating the slope), then wondered what to do with the other two - where were the points for those?  What are the forms for those?  They had NO concept that the SAME line could be written three different ways and/or how to go between the three forms.  Where's the calculator button for that?  Is the "b" in y=mx+b the same as the one in Ax+By=C?

 

They were given a function h(x) drawn and told w(x) = h(x+5) - 4 and were asked to draw h(x) and explain the shifts.  How could they do that without numbers?  What do they put into the calculator for the "h?"

 

They were told to sketch the graph showing a hot cup of coffee cooling exponentially if the room temp was 70 degrees.  How could they draw a graph without more numbers?

 

They were told to solve r^2 + 4r - 2 = 2 (or something like that).  What did that mean?  How can you put that into the calculator?  Are we supposed to find the zeros OR the intercepts or graph it or what?  It doesn't make sense.

 

ALL of these questions should have been easy IMO - considering they are currently taking the class (having covered the material), got to have a formula sheet for the test, and got to have a packet explaining parent graphs.

 

IMO the tests our school uses are SUPER EASY, esp since questions too many kids miss get axed from future tests, yet the kids still struggle.  Why?  They have no understanding of the concepts.

 

Some of it is due to kids not paying attention or not doing their homework effectively.  Some of it is due to our book which is some of the new math teaching kids to follow steps, but they rarely "get" the steps.  And a good part of it is due to not understanding the basics of math.

 

It frustrates me because there are several talented kids who could do it if given the opportunity.  It's really common that many understand after I get to explain things (though they still need practice, of course).  But for a test... there's not any "teaching" I can do, so it gets frustrating when I want to assist, but can't (aside from rewording for them).

 

And as an aside it was also a crappy day for me health-wise, so that probably added to my frustration as all of this is nothing new to be honest.  I deal with it often.

 

Sometimes I think I should either give up my job or go strictly toward tutoring, but on the other hand, I love the camaraderie with the kids (they appreciate it too) and other teachers - plus I also do science and enjoy that...

 

But the math dept stuff/fight is front and center now and I feel "my" side is losing (sigh).  I see the future of our country math-wise and it's not a pretty scene.  I'm so glad many of us are homeschooling (or afterschooling) to keep math knowledge alive.

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I am all for calculators in their time and place.  They can make difficult problems far more easy to do IRL.  Weird functions can be easily graphed and differentiated.  Complex calculations can be done at our fingertips quickly.  I don't feel we need to go back to the stone age.  I just think kids should learn MATH first.

 

I think kids should actually understand addition, subtraction (negatives essentially meaning a change in direction), multiplication, and division.

 

I think kids should grasp fractions and how they work with all of those functions to the point of being able to explain them.

 

I think they should grasp that square roots are the sides of squares with that area, that exponentials are a way for compounding or depreciating things (and what that means), that division by zero doesn't make sense, and what inequalities mean.  I want them to look at graphs and comprehend them - being able to explain them.

 

Whatever they are doing, I want kids to be able to explain it to me what it means in basic English.  It's how I ALWAYS start my class since I'm coming in subbing and need to see where they are.  It's rare that they can do this, so I start there - many times even having to back up because they missed foundational things.  But I can't do this on testing days.

 

On today's test they were given two points and had to create a line in three forms - y intercept, point slope, and standard.  Way too many kids got the first (if they didn't make a stupid mistake calculating the slope), then wondered what to do with the other two - where were the points for those?  What are the forms for those?  They had NO concept that the SAME line could be written three different ways and/or how to go between the three forms.  Where's the calculator button for that?  Is the "b" in y=mx+b the same as the one in Ax+By=C?

 

They were given a function h(x) drawn and told w(x) = h(x+5) - 4 and were asked to draw h(x) and explain the shifts.  How could they do that without numbers?  What do they put into the calculator for the "h?"

 

They were told to sketch the graph showing a hot cup of coffee cooling exponentially if the room temp was 70 degrees.  How could they draw a graph without more numbers?

 

They were told to solve r^2 + 4r - 2 = 2 (or something like that).  What did that mean?  How can you put that into the calculator?  Are we supposed to find the zeros OR the intercepts or graph it or what?  It doesn't make sense.

 

ALL of these questions should have been easy IMO - considering they are currently taking the class (having covered the material), got to have a formula sheet for the test, and got to have a packet explaining parent graphs.

 

IMO the tests our school uses are SUPER EASY, esp since questions too many kids miss get axed from future tests, yet the kids still struggle.  Why?  They have no understanding of the concepts.

 

Some of it is due to kids not paying attention or not doing their homework effectively.  Some of it is due to our book which is some of the new math teaching kids to follow steps, but they rarely "get" the steps.  And a good part of it is due to not understanding the basics of math.

 

It frustrates me because there are several talented kids who could do it if given the opportunity.  It's really common that many understand after I get to explain things (though they still need practice, of course).  But for a test... there's not any "teaching" I can do, so it gets frustrating when I want to assist, but can't (aside from rewording for them).

 

And as an aside it was also a crappy day for me health-wise, so that probably added to my frustration as all of this is nothing new to be honest.  I deal with it often.

 

Sometimes I think I should either give up my job or go strictly toward tutoring, but on the other hand, I love the camaraderie with the kids (they appreciate it too) and other teachers - plus I also do science and enjoy that...

 

But the math dept stuff/fight is front and center now and I feel "my" side is losing (sigh).  I see the future of our country math-wise and it's not a pretty scene.  I'm so glad many of us are homeschooling (or afterschooling) to keep math knowledge alive.

:grouphug:  :grouphug:  :grouphug:

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I have a policy in my classes that answers that defy common sense will not receive partial credit, no matter how much of the problem is correct.

 

For example: If I tell you a bank account of $1500 is invested at 3% interest, and ask how much is in it after 5 years, any answers LESS than $1500 receive an automatic 0. 

 

Quite honestly I've thought about awarding negative points for those (just to emphasize that sometimes it is more important to say "I have no idea" than to say something that you know is wrong), but I have not yet gone that far. 

 

I wish we could do this.  It might help.  It's a good idea IMO.

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OK, I'm old, but I was doing through multivariable calculus without a calculator.

 

Generations of us managed to learn Calculus without the use of a calculator.  What is interesting though is that back in the day my Calc/DE classes were very proof oriented. That certainly is no longer the case in a generic Calc class.

 

That said, don't make me perform interpolations using trig tables!  :tongue_smilie:

 

They do not get the slightest feel for when their calculator might be wrong due to operator error or otherwise.

 

They could be adding 4+5+7 and get 356 (somehow) and see nothing wrong with it.  Ditto that with thinking 400 could be 10% of 40 if they forget to push the % button.

 

They can be graphing lines and totally not get that they missed a negative when they see an increasing line, but the problem had a negative slope.

 

They can square -7 and argue with me that it HAS to be -49 as that's what their calculator is telling them.

 

There are just far too many foundational basics that they are missing IMO.

 

Sometimes I'll admit to wondering if the (calculator-loving) teachers themselves know these foundational basics or not.  I think they do - honestly - but how do they not see that (too much) calculator usage is not passing that knowledge on?

 

I always tried to teach common sense tests to help avoid operator error.  But it is a huge issue!

 

Several years ago, I tried to help a girl in a calculator based algorithmic class at the local high school.  I could not do it. Later she found a good instructor at the CC who taught her the hows and whys of College Algebra, not just the algorithms.  She said it stuck with her--unlike learning a series of key strokes.

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Oh gosh, for most kids I agree on the calculator stuff, but for dd15 who has some kind of undiagnosed not-quite-dyscalculia, they are the world's greatest blessing. The calculator lets her feel more confident. She feels good about being able to use the calculator. Without a calculator she would drown. As it is, she only just has her nose above water.

 

But yeah, that's not most kids. Ds isn't allowed near one.

 

I've worked with students like this and they rarely have problems understanding the concepts when they are explained well to them.  They can have issues with the actual calculations - so yes - the calculator is great for them, but IMO, they still do FAR better when they understand WHY they are pushing the buttons they are pushing.

 

When I drew out squares to show completing the square to the learning support kids, it clicked for them - "oh, that makes sense."  We could then move on to the short cut for finding it because it made sense with what was happening.  When having to do the calculations solely they often forgot which order to do things in. (What gets halved?  Squared?  Where do you put the numbers? Are they added or subtracted?  It was too much to remember in rote order.)  If they knew how to do it via drawing, they could fall back on that when/if they got stuck.  Some did.

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That is how it was for my older kids in high school. It is the main reason I won't do public school again. The teachers literally did not know any math. The teachers just kept telling them to plug it in on the calculator. And my daughter was in Mu Alpha Theta and they did nothing math related. I heard it is the same thing in middle school. I had to actually teach the subjects each summer. I would say re-teach, but I feel it was never taught in the first place.

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I'm an SAT/ACT tutor who specializes in working with LD kids.  I have a student now who CANNOT solve problems without his calculator even when a) it's faster and easier to just do the math and b) the answer choices on the ACT appear in fractions/radicals/exponents and all of his answers are in decimals.  I am having to undo a lot of things he's learned at school, and I'm having to ask him to do fractions worksheets since he has no recollection of how to work with them.  Grrr....  It's all done him such a disservice.  It makes me angry on his behalf!

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It seems all the major publishers introduce calculators in 3rd grade now, so no one has to master even basic arithmetic. Students do not have any idea what is happening to numbers when they multiply. Forget fractions, decimals and percents.

 

Yup.  I volunteer as a math tutor for GED students.  The teacher complains that the 3rd graders now use their phone calculators.  And all the students who struggle with Algebra do so because they don't understand fractions, decimals, percents.  The first thing I ask a new student is: what is 8x7?  I think I can predict their ability to pass the GED based on their answer.

 

At CC, my son used a graphing calculator for Statistics and Calc 1.  Now, he is a freshman at an engineering school.  He complained to me a little while ago that they are only allowed to use (I gather) scientific calculators on their exams (can't remember if it was Calc 2, Chem, Physics, or all).  I thought it was a great idea.

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I'm an SAT/ACT tutor who specializes in working with LD kids.  I have a student now who CANNOT solve problems without his calculator even when a) it's faster and easier to just do the math and B) the answer choices on the ACT appear in fractions/radicals/exponents and all of his answers are in decimals.  I am having to undo a lot of things he's learned at school, and I'm having to ask him to do fractions worksheets since he has no recollection of how to work with them.  Grrr....  It's all done him such a disservice.  It makes me angry on his behalf!

 

I hate to "like" these as I really don't, but I certainly do understand them.  It's exactly what I work with and it does come up that way from the middle school at least.

 

Some teachers - esp the older ones - do still work on math knowledge, but the "calculator only" ones are rather easy to spot later on when their kids don't know much.  It boggled my mind when I saw one teacher teaching the quadratic formula only via calculator and trying to teach kids "steps" to know where to put parentheses.  Steps for parentheses?  Many of those can be done via mental math FAR more quickly and accurately.  Well, they can IF one knows what -2 squared (etc) is... or proper order of operations.

 

There are many times I'd love to run my own math classes, but not with all the burdens our ps teachers have to deal with besides teaching - and I'm not really into the "same stuff, every day" deal.  I'm too much of a travel junkie and need my fixes, plus I love variety - alg one day, pre-calc the next, chem after that, etc.

 

Many times I even kind of force kids to integrate math and science - correctly.   :D

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Not only have a found that many of my college students do not know basic math--like 50% is the same as 1/2, they have trouble using any calculator except the ONE calculator that they were trained to use.  If the exponent key is in a different location than it was on the calculator they are used to, they have no clue what to do.  It isn't that they are dependent on calculators, they are dependent on A calculator.  Then when we try to teach something in business like how to set up an Excel spreadsheet to do calculations, they have no idea what to do, because they don't understand basic mathematical operations.

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Not only have a found that many of my college students do not know basic math--like 50% is the same as 1/2, they have trouble using any calculator except the ONE calculator that they were trained to use.  If the exponent key is in a different location than it was on the calculator they are used to, they have no clue what to do.  It isn't that they are dependent on calculators, they are dependent on A calculator.  Then when we try to teach something in business like how to set up an Excel spreadsheet to do calculations, they have no idea what to do, because they don't understand basic mathematical operations.

 

This would be an interesting experiment to try, but I don't know that I want to find out the answer.  Ours use TI 83 or 84.  The school provides 83, but some students buy 84.  Those two are similar enough that I don't think it matters.

 

Our kids go back and forth enough to know that 0.5 = 1/2, but many would get stuck knowing either are 50%.  They could take 1/2 of 6, but would need calculators to multiply 0.5x6 or to get 50% of 6, so their knowledge is pretty limited.

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I hate to "like" these as I really don't, but I certainly do understand them.  It's exactly what I work with and it does come up that way from the middle school at least.

 

Some teachers - esp the older ones - do still work on math knowledge, but the "calculator only" ones are rather easy to spot later on when their kids don't know much.  It boggled my mind when I saw one teacher teaching the quadratic formula only via calculator and trying to teach kids "steps" to know where to put parentheses.  Steps for parentheses?  Many of those can be done via mental math FAR more quickly and accurately.  Well, they can IF one knows what -2 squared (etc) is... or proper order of operations.

 

There are many times I'd love to run my own math classes, but not with all the burdens our ps teachers have to deal with besides teaching - and I'm not really into the "same stuff, every day" deal.  I'm too much of a travel junkie and need my fixes, plus I love variety - alg one day, pre-calc the next, chem after that, etc.

 

Many times I even kind of force kids to integrate math and science - correctly.   :D

I think the calculator folks are the ones who also advocate the "why memorize when you have Google" approach to education.  Sorry, but Google doesn't help if you don't know what questions to ask it!  Having knowledge IN your head makes you able to both learn more and solve problems efficiently.  Sure you don't want to run your own classes?  :)

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I think the calculator folks are the ones who also advocate the "why memorize when you have Google" approach to education.  Sorry, but Google doesn't help if you don't know what questions to ask it!  Having knowledge IN your head makes you able to both learn more and solve problems efficiently.  Sure you don't want to run your own classes?   :)

 

They are definitely of the same mindset.  It's a far cry from my college physics days when all we were allowed as a given was F=ma and had to derive everything else we wanted to use (once it was derived for a test we could use it thereafter).

 

I love google and use it often.  I love what calculators can do in making many parts of life easier.  But I still prefer when humans have knowledge and just use tools to augment it.

 

I occasionally run my own classes when teachers leave for maternity or military reasons.  It is fun/enjoyable/rewarding, but a bit of that would change if I had to go full time.  I really do get away with a lot as a sub (doing things my way), but wouldn't be able to do the same joining the system.  They have specific examples they must use, specific problems to do (and skip), ways they have to let the kids do things, and aren't allowed much in free thinking.

 

I take the book, look at it, and totally do my own thing with those problems often making up my own extra examples to show variety, and connections, etc.  I was a bit worried that the math teachers would be upset, but those I've talked with tell me they wish they could do the same (those who aren't calculator only folks anyway).  The calculator only folks just shrug and let me do what I want.

 

Part of the math dept "issue" is that the calculator only folks have started skipping some of the problems they don't like, so I might have started a bad thing overall to be honest.  The "play by my own rules" that I've been using to go into more depth they are starting to toy with to offer less.  It really is frustrating on many levels and makes me consider giving it up now that my boys have graduated and moved on.

 

Then there's the student who came up to me as I was leaving McD's Friday night and offered a hug plus happily introduced me to her family.  I met her in 8th grade (one of those long term deals as I rarely do middle school, but they needed someone who could do Alg for 12 weeks).  She's now a junior in Pre-Calc and wants to head Pre-med.

 

I enjoy the connection with the kids and it would be difficult to let that go.

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At my kids college they aren't allowed to use a calculator for their Calculus class.

 

And this is a big part of the current "fight."  Take quadratic functions for example.  We are supposed to teach completing the square, factoring, the quadratic equation, and graphing as ways to solve these.  All of them have their uses.

 

The calculator only teachers tell their kids to put the formula into the graphing calculator, then use the zeros function to get their answers.  They may, or may not, have briefly gone over the other methods.

 

It works, of course, and kids like it, but they end up missing out on all the math.

 

Then, what happens when they get to a calc class and can't use calculators?  It might only happen to a small overall percentage of them, but those are likely to be our top academic students... there's no reason at all that they shouldn't have been exposed to math in high school to be ready for college instead of having to play catch up when the speed is already fierce.

 

Then multiply this by oodles of other examples I could have chosen.

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This would be an interesting experiment to try, but I don't know that I want to find out the answer.  Ours use TI 83 or 84.  The school provides 83, but some students buy 84.  Those two are similar enough that I don't think it matters.

 

I have a TI 36X SOLAR (can't forget the solar!) from high school I still use when I'm feeling lazy. You can borrow it and see what hijinks ensue. ;)

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And this is a big part of the current "fight."  Take quadratic functions for example.  We are supposed to teach completing the square, factoring, the quadratic equation, and graphing as ways to solve these.  All of them have their uses.

 

The calculator only teachers tell their kids to put the formula into the graphing calculator, then use the zeros function to get their answers.  They may, or may not, have briefly gone over the other methods.

 

It works, of course, and kids like it, but they end up missing out on all the math.

 

Then, what happens when they get to a calc class and can't use calculators?

 

Or, heaven forbid, they encounter a problem where the coefficients are SYMBOLS and they have to manipulate the quadratic formula to obtain a symbolic answer!

In our physics classes, students struggle immensely with using symbols instead of numbers. They can manipulate numbers in their calculator - but if the equation is purely symbolic, that simply doe snot work and they MUST know how to do the math.

 

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Yup.  I volunteer as a math tutor for GED students.  The teacher complains that the 3rd graders now use their phone calculators.  And all the students who struggle with Algebra do so because they don't understand fractions, decimals, percents.  The first thing I ask a new student is: what is 8x7?  I think I can predict their ability to pass the GED based on their answer.

 

At CC, my son used a graphing calculator for Statistics and Calc 1.  Now, he is a freshman at an engineering school.  He complained to me a little while ago that they are only allowed to use (I gather) scientific calculators on their exams (can't remember if it was Calc 2, Chem, Physics, or all).  I thought it was a great idea.

I have been struggling with my 10 yr old since he has been home because he used calculators all through 3rd and 4th grade.

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DH teaches statistics at a university that bills itself as "one of the finest in the country." 

 

He regularly comes home with stories like these. He's troubled by the kids who don't understand proportions and percents. He's flummoxed by the kids who multiply 3 by 0.10 in their calculators. (This happened three times in one day. He lost it that day.)

 

There is a profound disservice being done to children with regards to mathematics education. I'm not sure where that disservice begins, or how to correct it. I suspect there too much pressure for a correct answer, rather than correct thinking. While the current common core prescriptions aren't perfect, the increased emphasis on explaining how answers are obtained is a welcome change from simply presenting an answer.

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DH teaches statistics at a university that bills itself as "one of the finest in the country." 

 

He regularly comes home with stories like these. He's troubled by the kids who don't understand proportions and percents. He's flummoxed by the kids who multiply 3 by 0.10 in their calculators. (This happened three times in one day. He lost it that day.)

 

There is a profound disservice being done to children with regards to mathematics education. I'm not sure where that disservice begins, or how to correct it. I suspect there too much pressure for a correct answer, rather than correct thinking. While the current common core prescriptions aren't perfect, the increased emphasis on explaining how answers are obtained is a welcome change from simply presenting an answer.

 

It is sad when I think of our school as being normal, though by all measures we are right there at the 50% (or close to it) mark.

 

I've posed the idea before of separating levels of Alg with lower levels (non college-bound) having more calculator use and higher levels (college bound) getting less at least for major parts, though still learning how to use them for things like zeros.

 

I was told that "Algebra is Algebra," so there's no need to differentiate it into levels.   :glare:

 

Levels, like with Bio, History, English, or anything else we teach, would allow us to go into more depth for those heading to math heavier fields.  I honestly do NOT comprehend why they wouldn't want to go that route.   :banghead:

 

More than three students in our classes would need their calculator to do 3 x 0.10.  It has a decimal in it!

 

And yes, I fall on the "pro" side when it comes to recent testing changes.  It has forced our school to add more into the curriculum - more that many would consider "basics!"  It wasn't too many years ago that we totally skipped covering circles in geometry. 

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It is sad when I think of our school as being normal, though by all measures we are right there at the 50% (or close to it) mark.

 

I've posed the idea before of separating levels of Alg with lower levels (non college-bound) having more calculator use and higher levels (college bound) getting less at least for major parts, though still learning how to use them for things like zeros.

 

I was told that "Algebra is Algebra," so there's no need to differentiate it into levels.   :glare:

 

Levels, like with Bio, History, English, or anything else we teach, would allow us to go into more depth for those heading to math heavier fields.  I honestly do NOT comprehend why they wouldn't want to go that route.   :banghead:

 

More than three students in our classes would need their calculator to do 3 x 0,10.  It has a decimal in it!

 

And yes, I fall on the "pro" side when it comes to recent testing changes.  It has forced our school to add more into the curriculum - more that many would consider "basics!"  It wasn't too many years ago that we totally skipped covering circles in geometry. 

 

Testing changes seem to be moving in the right direction.  Now if only the instruction and developmentally appropriate material could be done better....I think the cart is still before the horse at the moment.   Sadly, a lot of kids are rushed through the foundational skills introduced in elementary and frequently the instructor is not terribly conversant in math.  Instruction is poor, comprehension and mastery are shaky but kids are able to sort of fake their way through because the math itself is not as complex.  That comes back to bite everyone as they move into higher math.

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  • 3 weeks later...

Unfortunately, the pro-calculator (and more) side of the fight won.

 

We now are supposed to teach kids solely to pass our Keystone Alg test.  It's mostly multiple choice.  Our number one method is to tell them to plug in numbers (on the calculator) and see if they work.  If not, it's the wrong choice.  Forget solving the equations to find the right answer.

 

Then too, I've been told curricula is getting cut (but they couldn't say exactly what) to match the test.  This won't necessarily be a problem if the test covers everything.  I can hope.

 

I feel for the kids who want to do more in math in college.  I really, really do.

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Unfortunately, the pro-calculator (and more) side of the fight won.

 

We now are supposed to teach kids solely to pass our Keystone Alg test.  It's mostly multiple choice.  Our number one method is to tell them to plug in numbers (on the calculator) and see if they work.  If not, it's the wrong choice.  Forget solving the equations to find the right answer.

 

:banghead:

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Unfortunately, the pro-calculator (and more) side of the fight won.

 

We now are supposed to teach kids solely to pass our Keystone Alg test. It's mostly multiple choice. Our number one method is to tell them to plug in numbers (on the calculator) and see if they work. If not, it's the wrong choice. Forget solving the equations to find the right answer.

 

Then too, I've been told curricula is getting cut (but they couldn't say exactly what) to match the test. This won't necessarily be a problem if the test covers everything. I can hope.

 

I feel for the kids who want to do more in math in college. I really, really do.

And people wonder why I don't just send my kids to school to be educated...

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Maybe this is mentioned up thread, but what math curriculums do you recommend for those of us starting out? I am particularly torn between the whole "conceptual vs. traditional" thing. I'd love to hear your advice!

 

I'm of the belief that it's not really the curricula that matters.  It matters that your student learns FROM that curriculum.  Try something that looks good to you (online samples can be good) to see if it works.  Don't be married to it if it doesn't.  Different students in the same family can prefer different curricula.

 

Learning math is not just rote memorization (though that can help with basic math facts).  It's knowing that 5x4 means five groups of four and is a quicker form of addition (in a way).  It's knowing that negative doesn't mean "bad," it means the opposite direction.  Later on it's recognizing that square roots are the sides of squares with a certain area (square root of 9 = 3 means a square with an area of 9 has a side length of 3).  When setting up and SOLVING equations they understand WHY it's being done as it is - not just memorizing steps.  It's understanding that trig functions are triangle ratios and slopes are rate of change.

 

Many kids do best when taught how and why.  A few do best when they can play with it and figure it out themselves.

 

When they truly know concepts, they can figure out the unknown.  When they are memorizing steps, they often will later forget which steps to do when and get confused.

 

Calculators as an aid after learning concepts are nice.  Calculators to learn to plug in steps are horrid.

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Unfortunately, the pro-calculator (and more) side of the fight won.

 

We now are supposed to teach kids solely to pass our Keystone Alg test. It's mostly multiple choice. Our number one method is to tell them to plug in numbers (on the calculator) and see if they work. If not, it's the wrong choice. Forget solving the equations to find the right answer.

 

Then too, I've been told curricula is getting cut (but they couldn't say exactly what) to match the test. This won't necessarily be a problem if the test covers everything. I can hope.

 

I feel for the kids who want to do more in math in college. I really, really do.

Oh my.

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and then we get them at university and they bitch at us because they don't feel they should be in remedial math.

 

well, you shouldn't. except your school lied to you and told you that you were learning math. Congratulations, you placed out of calculator manipulation 101.

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Unfortunately, the pro-calculator (and more) side of the fight won.

 

We now are supposed to teach kids solely to pass our Keystone Alg test.  It's mostly multiple choice.  Our number one method is to tell them to plug in numbers (on the calculator) and see if they work.  If not, it's the wrong choice.  Forget solving the equations to find the right answer.

 

Then too, I've been told curricula is getting cut (but they couldn't say exactly what) to match the test.  This won't necessarily be a problem if the test covers everything.  I can hope.

 

I feel for the kids who want to do more in math in college.  I really, really do.

 

I really don't understand this mentality.  Sure it is an ok strategy to hold in reserve if you are having trouble with solving a problem.  But really, it's faster to just solve the problem in most cases than it is to try to plug a bunch of possibilities into the equation.  Not to mention the fact that one way actually teaches math and the other teaches calculator operation.

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I really don't understand this mentality.  Sure it is an ok strategy to hold in reserve if you are having trouble with solving a problem.  But really, it's faster to just solve the problem in most cases than it is to try to plug a bunch of possibilities into the equation.  Not to mention the fact that one way actually teaches math and the other teaches calculator operation.

 

I don't get it either and never have aside from the learning support kids who really don't understand the abstract concepts of most Alg yet have to take the test anyway.

 

It gets better.  In my classes later this week I get to do test review, then a team test (groups of 3 or 4 work together on team tests, then share the grade - they all have to agree on the answers).  I've been told to give very good hints on the test as the goal for that is to make sure they can work through it.

 

They have 3 - 4 students working on the problems and STILL need ample hints.  Is there any wonder why?

 

This is all normal (sigh).  I'm just dismayed to be on the losing side of this fight - even though I've been watching it come.

 

The mentality on the other side is that life is changing, computers are taking over, and kids merely need to know how to use them.  All calculations will be on machines, not done by hand.  We're told it's very akin to how there are few harness makers anymore.  So much that used to be done by hand no longer is.

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The mentality on the other side is that life is changing, computers are taking over, and kids merely need to know how to use them. All calculations will be on machines, not done by hand. We're told it's very akin to how there are few harness makers anymore. So much that used to be done by hand no longer is.

The automation machines need to be programmed too. Being able to use a calculator doesn't mean the skill will transfer to programming a CNC or other automation machine :P

I used to do Finite Element Modelling. I still need to make sure that the stress diagram I am getting makes sense conceptually and I had to do some free body diagram calculations to verify computer output.

Kids who only know how to use the computers aren't going to be able to climb the corporate ladder fast. Punching calculators most of the time also takes the fun out of math.

Besides if kids are only taught to rely on punching calculators, how would they know if software like TurboTax compute their tax wrongly.

 

When my kids were in PS, my older was told to eliminate two out of 4 MCQ answers for being obviously wrong and then pick one of the two leftovers. He wasn't allowed calculator use for state testing in 2nd, 3rd and 4th.

 

ETA:

It seems common core math tests has a calculator section from 6th grade.

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I don't get it either and never have aside from the learning support kids who really don't understand the abstract concepts of most Alg yet have to take the test anyway.

 

It gets better. In my classes later this week I get to do test review, then a team test (groups of 3 or 4 work together on team tests, then share the grade - they all have to agree on the answers). I've been told to give very good hints on the test as the goal for that is to make sure they can work through it.

 

They have 3 - 4 students working on the problems and STILL need ample hints. Is there any wonder why?

 

This is all normal (sigh). I'm just dismayed to be on the losing side of this fight - even though I've been watching it come.

 

The mentality on the other side is that life is changing, computers are taking over, and kids merely need to know how to use them. All calculations will be on machines, not done by hand. We're told it's very akin to how there are few harness makers anymore. So much that used to be done by hand no longer is.

I was flipping through a Khan Academy discussion board yesterday and had to comment on one thread. Kid #1 was trying to figure out 30% of 6. He was confused and was asking if 0.018 was correct. Kid #2 swooped in and persuasively explained how to solve it. Except his answer was 180%.

 

Not only was his answe off, but he was convinced that a percentage of a number was another percentage.

 

Neither had the number sense to realize that 1/3 of 6 is 2 so 30% should be just under 2.

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I was flipping through a Khan Academy discussion board yesterday and had to comment on one thread. Kid #1 was trying to figure out 30% of 6. He was confused and was asking if 0.018 was correct. Kid #2 swooped in and persuasively explained how to solve it. Except his answer was 180%.

 

Not only was his answe off, but he was convinced that a percentage of a number was another percentage.

 

Neither had the number sense to realize that 1/3 of 6 is 2 so 30% should be just under 2.

I think this problem is endemic in math instruction in the US--kids are taught to manipulate numbers without ever really gaining an understanding of what they are doing. I think the common core standards attempt to address this, but I doubt they will do any good when the teachers themselves often lack a foundation of conceptual understanding.

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I think this problem is endemic in math instruction in the US--kids are taught to manipulate numbers without ever really gaining an understanding of what they are doing. I think the common core standards attempt to address this, but I doubt they will do any good when the teachers themselves often lack a foundation of conceptual understanding.

 

I haven't followed the Common Core debate wrt math standards.  The few worksheets I've seen appear to me as if they are making an effort to try to get students to think about the meaning of the operations.  But where I think they fall short is that they ask for overly detailed explanations of things that seem quite self evident from very young students.  (Reminds me of the way that new math was implemented with an emphasis on set theory that wasn't appropriate for the youngest grades.)

 

The other issue I have is that often, it seems as if there is only one answer that is acceptable.  So if the student is creative or has an innate number sense that they cannot articulate yet, they are penalized.  Especially if the teacher doesn't know math well enough to understand what the student is trying to get at.

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