More news about poor math education in the USA

[Catherine]

This is news to none of us, I am sure:

 

http://www.nytimes.com/2015/04/26/opinion/sunday/nicholas-kristof-are-you-smarter-than-an-8th-grader.html

 

The editorialist is frustratingly short of ideas for improving math education in the USA.  

 

I am off to ask my eighth grader to answer the questions he poses.  I'll let you all know how he does.

[creekland]

Definitely not news here and the majority of 9th graders where I work wouldn't be able to answer the questions either.  I'm not even sure the majority in the higher grades would do any better, esp the degree question, to be honest.  It's pretty sad.

[8filltheheart]

My 7th grader just worked out the 3 sample problems correctly. That so few kids are able to solve those is pretty darn sad. :eek: Those were incredibly easy problems!

 

FWIW, that logic question is in the movie the Labyrinth. :) (can't get the YouTube link to work. Just google Labyrinth 2 door riddle if you want to see the scene.)

[Catherine]

He got them all right!  And the logic problem.  I am relieved-he is my weakest math student.  I think I need to re-read Knowing and Teaching Elementary Mathematics.  I love that book.

 

[creekland]

Assuming this isn't popular on FB, I'll try to remember to ask the questions in my classes on Wed.  I'm not totally sure what level all the classes are at, but I know I at least have some of our top math students in College Alg (a DE course).  If any group has promise, the kids in there would be it.

[mom2bee]

Its sad that so few of the US children polled could answer those questions. :(.

On the flip side, I was a little stumped by the riddle, but I got it after a few minutes.

[Arcadia]

The first question's answer is quickly deduced based on mean.

 

The second question requires the student to remember what an analog clock face look like. I was joking some time ago with my 9 year old that he need to wear his analog watch to exams next time just to look at the clock face. He has problem with time (including time management)

 

Labyrinth (David Bowie) was one of those intense movies that I watched as a teenager. I was amused by the Escher style stairs in the movie.

[maize]

Dd11 got the first two, but needed my help setting up the third.

[8filltheheart]

I just laughed bc my kids love that movie and when I read it, they all said, "she is asked that exact question in Labyrinth." Knowing the answer bc you know the answer doesn't really count, does it. ;) Though they quoted her last line, "I think I'm getting smarter!" So maybe it does! LOL!

 

Some of my kids have worked through Labyrinth of Reason which has some good logic puzzles in it. http://www.amazon.com/Labyrinths-Reason-Paradox-Puzzles-Knowledge/dp/0385242719

[Arcadia]

Some my kids have worked through Labyrinth of Reason which has some good logic puzzles in it. http://www.amazon.com/Labyrinths-Reason-Paradox-Puzzles-Knowledge/dp/0385242719

Thanks. Adding that to books to look out for at library :)

[creekland]

ps  For the length of wood question, it might be important that they can use their calculators for the math, esp those below the College Alg level.  College Alg should be able to do the math with/without calculators.  Even then I'm sort of expecting them to solve for x correctly and still get the answer incorrect as they probably aren't inclined to actually finish the question.

[8filltheheart]

ps For the length of wood question, it might be important that they can use their calculators for the math, esp those below the College Alg level. College Alg should be able to do the math with/without calculators. Even then I'm sort of expecting them to solve for x correctly and still get the answer incorrect as they probably aren't inclined to actually finish the question.

Why the heck would they need a calculator to answer that question? My 7th grader did it in her head while making a sandwich for lunch! Yikes! 40-8 divided by 4 requires a calculator? ETA: I went back and looked at the article. The multiple choice answers weren't given. I could see kids hurrying not answering the real question if 8 was included in the answers.

Edited April 27, 2015 by 8FillTheHeart

[Arcadia]

ps  For the length of wood question, it might be important that they can use their calculators for the math, esp those below the College Alg level.  

 

no calculators required :huh:

 

4x + 8 = 40

4x = 32

x = 8

[creekland]

Why the heck would they need a calculator to answer that question? My 7th grader did it her head while making a sandwich for lunch! Yikes! 40-8 divided by 4 requires a calculator?

 

About two weeks ago I ended up having to let way too many 9th graders use a calculator to figure out 28x7 = 7x __.  It was a science class, but still... The vast majority of all three classes I had needed help figuring out they could solve this without a calculator... and some never did come to that conclusion, so I ended up telling them, "Fine, use your calculator." (sigh)

 

And then about half who needed to use their calculator looked at me and said, "That can't be right can it?  28 is in the first part of the question.  Is the answer 4?"  I'm thinking we need to give them some sort of credit for at least linking that 7x4=28.

 

In an Alg 2 class I've had to let them use calculators to figure out 4x100.  I can't count the number of times I've been told (-2)^2 is -4, etc.

 

It's pretty sad to see just how calculator dependent the younger generation is - and about half the teachers at our school see no problem with this.  That half is currently in charge of the dept.

[creekland]

no calculators required :huh:

 

4x + 8 = 40

4x = 32

x = 8

 

With calculators many should be able to solve this IF they figure out how to set it up.  

 

But will they remember to plug that in to the two potential long sides to see which one is longer?  I'm expecting them to stop at 8 or to naturally assume the piece with the 2x in it has to be longer than anything with just x.  It won't matter that there's subtraction involved with the 2x.  Chances are that they won't catch that they can eliminate having to check the third option since it adds one less than the second.

[Meriwether]

Dd11 (almost 12) figured out all three math problems but not the logic problem. I don't think Ds10 could answer the math problems. Maybe I'll ask, but I would assume not.

[debi21]

I spent some time this spring observing in a 10th grade algebra 2 class. The teacher told me that a fairly accurate way to predict who would do well in the class was determining who knew their times tables (and therefore didn't need to use their calculators for basic multiplication) at the beginning of the year. The other major predicting factor seems to be students' ability with fractions, particularly finding a common denominator. Scary.

 

 

[Meriwether]

With calculators many should be able to solve this IF they figure out how to set it up.  

 

But will they remember to plug that in to the two potential long sides to see which one is longer?  I'm expecting them to stop at 8 or to naturally assume the piece with the 2x in it has to be longer than anything with just x.  It won't matter that there's subtraction involved with the 2x.  Chances are that they won't catch that they can eliminate having to check the third option since it adds one less than the second.

This is really sad.

[Catherine]

What you all are saying here reinforces my belief that the widespread math failure here in the US is a failure of the mathematics taught before 6th grade...IOW, arithmetic.  The thesis of Liping Ma's book is that one big difference between math education in China and math education here in the United States is that arithmetic is a subject deemed worthy of serious study in China, but here we consider it "baby math" and do not ensure that teachers fully understand it, so they cannot impart their understanding to students.  

[Meriwether]

Ds10 could not have figured these out on his own, but he figured them all out step by step with me. On the first one, for example, I had to ask him how he would write one number less than 2n. He did see right away that it couldn't be x+6 on the third one. And he said, "They probably want us to think that 2x-5 is bigger because it is 2x, so it probably isn't that one. Ironically, that was the easiest one for him to solve. He hasn't worked with setting up equations yet.

[creekland]

What you all are saying here reinforces my belief that the widespread math failure here in the US is a failure of the mathematics taught before 6th grade...IOW, arithmetic.  The thesis of Liping Ma's book is that one big difference between math education in China and math education here in the United States is that arithmetic is a subject deemed worthy of serious study in China, but here we consider it "baby math" and do not ensure that teachers fully understand it, so they cannot impart their understanding to students.  

 

IMO, the problem comes before we get them in high school and it's due to a lack of understanding math.   They can be decent at pushing buttons on a calculator and/or following step by step instructions, but they have a difficult time seeing any sort of big picture.  With the 28x7 = 7x __ problem, I first tried to explain it by telling them to think...  2x3 is the same as 3x what?  Most would look at me and go, "2x3=6.  Ok, hang on a second... 6/3 =..."  

 

They are missing entire concepts - or even that there is a concept.

 

In high school (or 7th/8th grade) they learn to solve for x, but many times they can't tell me what x is supposed to be once they have it.

 

As long as our state tests allow calculators, I doubt anything will change.

 

Then high school gets blamed.  Why?  Some problems can't be solved on calculators and the concepts we try to teach require an understanding of the actual math involved.  Teachers can pull kids along in class (team tests, homework completion grades, etc), but when it later comes to mixed tests (SAT/ACT or others) there are often huge issues.  Naturally it's the test's fault.

 

Then don't even get started with needing to use math in science.  Science teachers find themselves trying to teach the math - math they shouldn't have to teach, but they most certainly do have to.

 

The school I work at is an average public high school by pretty much all testing statistics.  Roughly 50% of schools are worse.

 

There's a reason I pulled my guys out to homeschool them.  Unfortunately youngest didn't like homeschooling.  He's been my least prepared (academically) for college and now is insisting on a major that doesn't need math beyond logic.  It's frustrating.

[Arcadia]

They can be decent at pushing buttons on a calculator and/or following step by step instructions, but they have a difficult time seeing any sort of big picture. With the 28x7 = 7x _ problem ...

Commutative property of multiplication was covered in 3rd & 4th grade. Really makes people wonder what went wrong in math instruction :(

 

I understand your frustration though. It is tough when the science teacher have to remediate math.

[8filltheheart]

Commutative property of multiplication was covered in 3rd & 4th grade. Really makes people wonder what went wrong in math instruction :(

 

I understand your frustration though. It is tough when the science teacher have to remediate math.

That is what I was thinking. My 3rd grader could easily answer Creekland's question. How on earth do they understand anything they are doing in upper level math? Even if they thought they needed to divide both sides by 7, they should still see the answer is 28???

 

Jeepers, examples like these DO make you wonder if the claims that anything done at home is better than the local school. The sample questions in that article are really basic questions. My 7th grader could have answered 2 of them in 4th grade. I don't think she could have answered the clock one then bc I don't think she knew a circle had 360 degrees. If she knew that back then ,she could have. The other 2 problems are similar to problems in HOE that she did back then.

[arliemaria]

What you all are saying here reinforces my belief that the widespread math failure here in the US is a failure of the mathematics taught before 6th grade...IOW, arithmetic.  The thesis of Liping Ma's book is that one big difference between math education in China and math education here in the United States is that arithmetic is a subject deemed worthy of serious study in China, but here we consider it "baby math" and do not ensure that teachers fully understand it, so they cannot impart their understanding to students.  

 

I've heard this book quoted many times, but have never looked at it.  I've been studying vintage texts on arithmetic study recently in preparation to teach my son.  Does Ma's book also fully expalin how arithmetic be taught or just simply proves her thesis?

[Ms.Ivy]

I've heard this book quoted many times, but have never looked at it.  I've been studying vintage texts on arithmetic study recently in preparation to teach my son.  Does Ma's book also fully expalin how arithmetic be taught or just simply proves her thesis?

 

Mostly it explains her thesis and her study results.  I love that book.... but if you're looking for something that will help you teach your son, I highly recommend Arithmetic for Parents by Ron Aharoni.  

[Catherine]

Mostly it explains her thesis and her study results.  I love that book.... but if you're looking for something that will help you teach your son, I highly recommend Arithmetic for Parents by Ron Aharoni.  

 

Agreeing...I'm not familiar with Arithmetic for Parents, but Ma's book doesn't necessarily tell you how to teach arithmetic, only shows painfully well how little some teachers understand basic math, fractions, concepts.  It did get me thinking more about trying to empart a grasp of concepts.  

[idnib]

While I am sadly not surprised about the U.S. results, I was surprised that only 53% of Singaporean 8th graders could answer the wood question. After we hear so much about their vaunted math education, I would have expected a higher number. And I say that as a big fan of Singapore Math.

[Farrar]

I let ds10 who is a young fifth grader and just starting pre-algebra try all three. The first one he got after a quick hint. The second one he absolutely couldn't do. That didn't surprise me - he's always been weak on everything geometric so even though we've covered that he ought to be able to give it a try, that's all stuff I know he needs to work more on. But the last one, the one that statistically was the "hardest" he solved super fast with zero help from me. That's so ds though - he finds hard problems easier and easy problems harder. Not that this one was all that hard. The problems he was doing this morning for review from Process Skills in Problem Solving were trickier, honestly.

 

Other ds10 probably couldn't have done any of them without a little guidance. Maybe, amusingly, the middle one he could have done. But he has done very little with variables yet.

 

 

[creekland]

 only shows painfully well how little some teachers understand basic math, fractions, concepts.  It did get me thinking more about trying to empart a grasp of concepts.  

 

 

I literally never get to our elementary or intermediate school to see what's going on, but I honestly have to wonder what is going on down there.  Obviously calculator training is, but another weird thing I see OFTEN is that many kids have no idea they can drop trailing zeros after decimal points.  If a problem says to add $25.00 to $9.82, they will type in everything from both numbers and not even realize they don't need the .00.  If I mention to them they can drop those digits they look at me like I'm crazy - and put them in anyway.

 

I suspect their calculator training consists merely of steps to follow too.

[madteaparty]

I'm not even going to try having DS take these, because frankly I don't need another reason to feel horrible about his academics and the cosmic repercussions thereof. The inadequate math instruction in the US has well and truly been beaten into me by this point, and fatigue is setting in. I've a French kid at home now and I can't say I'm super impressed with the math instruction there either.

[creekland]

I'm not even going to try having DS take these, because frankly I don't need another reason to feel horrible about his academics and the cosmic repercussions thereof. The inadequate math instruction in the US has well and truly been beaten into me by this point, and fatigue is setting in. I've a French kid at home now and I can't say I'm super impressed with the math instruction there either.

 

Remember that 50% of the schools are better than the one I work at.  ;)  And even at our school there are occasionally students who rise above "just" what they are taught.

 

There are still teens going out there and doing great things with their lives - even things that include math.

 

Not all, but the majority of exchange students we get are better at basic math though.  Our science curricula appears to cover more topics than theirs for the same age/grade as a general rule.

[Catherine]

Before nclb and full inclusion, the ele. students here did every chapter in the math text. Math class was daily. Students were scoring in the 90% iles on nationally normed achievement tests. The year nclb & full inclusion started, only 4 of the 13 chapters in the math texts were done...2 review, 2 new. Math was no longer daily. Students that previously scored in the 90% iles dropped to high 40% iles. Not enough material is taught to enable a child to score in the 'advanced' zone here on state testing.

 

Its not the teachers. They are competent. The results they obtained before nclb and full inclusion show that. They are being told what and when to teach. And that means many concepts necessary for college bound students are left out.

 I think there are probably many reasons that students here fail to learn even basic arithmetic a lot of the time.  But teaching is without question one part of it.  Have you actually spoken to an elementary school teacher about it, or read the book I mentioned?  Because my n of 2 teachers showed me that neither of them understand basic fractions and decimals.  The way they are made to teach is part of the issue as well, a big part.  Inadequate curriculum and completely inadequate prep time are part of the problem too.  But knowledge base is a real problem, IMO.

[creekland]

There were years where our students were taught that they didn't have to know how to do fractions as their calculator could always do them for them.

 

This "fact" doesn't work when one reaches algebra and needs to work with fractions containing variables.  (sigh)

 

I believe this gap is fixed now, but there's still little real knowledge in their minds.  At least we get to start with review rather than a brand new concept.

 

And conceptually?  I doubt they know WHY the "rules" are what they are, but we don't have time to teach those.  I make a couple of exceptions and often explain why we can't divide by zero and why we can't just add denominators.

 

Decimals and percents are definitely another area of concern.  There's a reason several places now tell you what 15% is (for a tip) or 30% off saves you (for a sale price).  Many kids I come in contact with have difficulty coming up with 10% of a number in their head.   :glare:   Once again, it's due to being trained for their calculators rather than trained in math.  They can do it (if taught).  

 

These things are rarely lack of ability.  

[Laura Corin]

ps  For the length of wood question, it might be important that they can use their calculators for the math, esp those below the College Alg level.  College Alg should be able to do the math with/without calculators.  Even then I'm sort of expecting them to solve for x correctly and still get the answer incorrect as they probably aren't inclined to actually finish the question.

 

Really?  I didn't do maths past age 16 and didn't teach it past age 15, and I did it quickly on a piece of paper.

 

ETA: should have read your responses above.

[creekland]

Really?  I didn't do maths past age 16 and didn't teach it past age 15, and I did it quickly on a piece of paper.

 

We grew up in a different era of math.  We didn't start using calculators in the very early elementary years as our school has them do now.

 

The pro-calculator group of teachers at our school reminds everyone that we no longer use slide rules and tables now either.  They feel kids are better knowing the technology of their generation than the nuts and bolts of being a harness maker in a world of automobiles.

 

I'm not in that group.  Most older teachers aren't.

[Farrar]

The calculator thing is pathetic. Just so pathetic. Only people who don't understand arithmetic can think it's not going to seriously undermine a math foundation to always use calculators.

[SparklyUnicorn]

We grew up in a different era of math.  We didn't start using calculators in the very early elementary years as our school has them do now.

 

The pro-calculator group of teachers at our school reminds everyone that we no longer use slide rules and tables now either.  They feel kids are better knowing the technology of their generation than the nuts and bolts of being a harness maker in a world of automobiles.

 

I'm not in that group.  Most older teachers aren't.

 

Yep.  Sat waiting for my kids in dance class once watching a girl do a page of long division using a calculator.  Maybe she was in 4th?  What's the point?!  She wasn't required to show any work.

 

Never used a calculator in math.  Not even in algebra.  Even with stuff like cosine we used charts at the back of the book. 

 

Now I see them on the school supply lists starting in 1st grade.  Ridiculous.  I do sometimes let my son use them in Algebra 2.  Mostly when the problem would just be ridiculous to calculate by hand.  Not impossible, but I don't want the assignment to take hours either. 

[Farrar]

My kids are in fifth grade. The first time I've really let them use calculators was this year while we were doing a unit on probability. Some of the problems we worked together had ridiculous sums. Sometimes I let them check their drill sort of work with a calculator if I don't have an answer key on hand. That's plenty of practice for learning how the technology works.

[SparklyUnicorn]

My kids are in fifth grade. The first time I've really let them use calculators was this year while we were doing a unit on probability. Some of the problems we worked together had ridiculous sums. Sometimes I let them check their drill sort of work with a calculator if I don't have an answer key on hand. That's plenty of practice for learning how the technology works.

 

I'm not looking forward to using a graphing calculator because I've never used one.  LOL 

[Laura Corin]

What I find interesting is this: whenever these international surveys come out, you get people saying that the tests are unfair because only certain schools are tested, and that in some countries only selective schools are chosen.  I haven't looked into this, but the young adult scores seem to back up the school scores, and neither the US nor the UK has anything to crow about.

[creekland]

My kids are in fifth grade. The first time I've really let them use calculators was this year while we were doing a unit on probability. Some of the problems we worked together had ridiculous sums. Sometimes I let them check their drill sort of work with a calculator if I don't have an answer key on hand. That's plenty of practice for learning how the technology works.

 

I have no problem with having kids use calculators to check their work at times.  It's quick and easy.  (They should also know how to check it without a calculator too.)

 

I have no problem with kids learning how to use calculators for trig functions, but I still want them to know what the trig functions mean.

 

I have no problems with kids using calculators to graph more difficult problems - AFTER they have learned how to graph well (our school actually does a reasonably decent job with graphing).

 

I have problems with young kids learning to use calculators instead of learning math (well).

 

Calculators as a tool are terrific.  Calculators as a crutch keep kids crippled.

[SparklyUnicorn]

What I find interesting is this: whenever these international surveys come out, you get people saying that the tests are unfair because only certain schools are tested, and that in some countries only selective schools are chosen.  I haven't looked into this, but the young adult scores seem to back up the school scores, and neither the US nor the UK has anything to crow about.

 

I don't know much about these tests, but I have read that only certain schools are tested.

 

And here, students are tested to death.  Frankly, I'd be less than enthusiastic to take yet another test for this purpose. 

[Ad astra]

While I am sadly not surprised about the U.S. results, I was surprised that only 53% of Singaporean 8th graders could answer the wood question. After we hear so much about their vaunted math education, I would have expected a higher number. And I say that as a big fan of Singapore Math.

 

Many students in East and Southeast Asia also struggle with math, especially in upper grades as math is incremental in nature. Their math curriculum itself might be superior to the traditional math texts in the U.S. but, according to my experience, their math instruction in the K-12 classroom is carried out in a very structured and unilateral way. There were over 60 students in my classroom alone when I went to school. (I think it's decreased to 40 per classroom recently since my home country has recorded the lowest birth rate in the world.) A lot of the actual study time was/is invested in practicing math drills and preparing for frequent standardized tests, and there's very little room for creativity or critical thinking on those test sheets. So, the average math standardized test scores of the Asian students might be higher than the ones in other countries, but it's hard to find those at the genius level.

 

The difference is that we were not allow to use a calculator in any K-12 setting, including all school tests and college entrance exams, even for differential and integral calculus, statistics and probability parts of the high school math courses. I used a calculator for the first time when I took multivariable calculus and other engineering classes in my freshman year of college. 

[Arcadia]

While I am sadly not surprised about the U.S. results, I was surprised that only 53% of Singaporean 8th graders could answer the wood question.

Singapore allows calculator use from 5th grade since 2008. It is incorporated into their math curriculum. What effect that has no one knows since the first batch would be taking their college entrance exams (IB or A Levels) this year and gets to use graphing calculators.

 

"In line with the phasing in of the revised Primary School Mathematics syllabuses, the Ministry of Education (MOE) will introduce the use of calculators at Primary 5 in 2008 and Primary 6 in 2009."

 

I have nothing against technology. I unscrewed my calculators when I was bored in school just to look at the circuit board. Still I feel starting calculator use at 10 years old is too soon and graphing calculator at 16 is not necessary. I do see a negative/crutch effect on my nephews and nieces that are currently schooling. That is just my opinion though.

[creekland]

What I find interesting is this: whenever these international surveys come out, you get people saying that the tests are unfair because only certain schools are tested, and that in some countries only selective schools are chosen.  I haven't looked into this, but the young adult scores seem to back up the school scores, and neither the US nor the UK has anything to crow about.

 

Sorry - missed this earlier due to posting at the same time.

 

Personally, I think our (US) top students can easily compete with other top students worldwide.  The students we get in as exchange students are all supposed to be relatively top students and they fit in well with ours (significantly better with languages though).  When I compare them to our average students they are (usually) far better, but what I don't get to do is compare average student to average student.

 

Since the worldwide tests also don't compare average students in other countries, they're still no help.  They're still testing top students elsewhere to all students here.

 

Here every single student who is not mentally significantly disabled has to take our tests - even those whose first language is not English and they haven't been here long enough to get a good command of the language.  In our state, every student who wants to graduate has to pass certain state subject tests.

 

Our exchange students tell me many such students wouldn't even be in (academic) school in their countries with some countries starting to differentiate students as early as 5th grade.

 

With this test in question, I wonder where they selected their 8th graders from.  Top schools or average stat schools?  And are all 8th graders still in these schools or not?

 

Even with all that, I feel that too much early calculator use and emphasizing that use over mental math is NOT a good thing - with exceptions for certain learning disabilities.  It doesn't matter which country is doing it.  Kids need to learn to think first IMO.

[Laura Corin]

With this test in question, I wonder where they selected their 8th graders from.  Top schools or average stat schools?  And are all 8th graders still in these schools or not?

 

 

We are talking at cross purposes.  Although the article talks about the test for 8th graders it also makes reference to the test for young adults:

 

The subject of this report is our nation’s millennials, those young adults born after 1980 who were 16–34 years of age at the time of the assessment.

 

This testing, one would assume, wouldn't be skewed by school type in different countries.  And the US and the UK still do fairly badly.

[amsunshine]

With this test in question, I wonder where they selected their 8th graders from.  Top schools or average stat schools?  And are all 8th graders still in these schools or not?

 

Yes, I wonder how students are selected to take the TIMSS.  I've never personally heard of any school near us administering this test.

[idnib]

I've also never used a graphing calculator. 

 

Based on the experience of my children's public-schooled friends, our district is still not using calculators up to 6th grade, at least. Not sure about past that.

[creekland]

I've also never used a graphing calculator. 

 

 

I learned how to use graphing calculators in order to teach at school.  They didn't come out until after I graduated from college.

 

Honestly?  They are nifty little gadgets allowing one to do far more difficult problems than can be done by hand.  Kids SHOULD know how to use them IMO - after they know the math and can do it by hand easily.

 

Their world will be filled with computers and machines.  Not knowing how to use graphing calculators or power point or other similar (common) deals could hinder them in their future pending what they choose to do.

 

I won't be able to run any of these problems by the College Alg classes today.  They're testing and the teacher expects the test to take the full time for some of the students.  They are not allowed extra time, so there's no way I want to use up some of what they have on these.  I suspect (hope?) the college alg students would do well on them.  It's one of the few math classes that's a very good one at our school (uses a traditional text rather than the new fuzzy math, and we're near the end of the semester).  MANY students tell me they feel they never knew a thing about Alg until they take this class.  AND there are plenty of segments in this class where the teacher doesn't allow calculators.  She and I are good friends... ;)  Interestingly enough, the math SAT score of students often increases by roughly 200 points with this class (according to guidance).

 

She also has an Alg 2 class where I'll be introducing inverses.  Perhaps I can slot a question or two in there - as a warm up.

[The Girls' Mom]

I am in my last week of College Math at our CC.  Although I placed higher, I didn't need much for math for my degree, so I picked the easiest class I could and still get the credit.  I was floored at how basic it is, and the kids in that class are STILL struggling.  You can see the teacher's frustration every class.  These kids can do nothing but plug things into a graphing calculator.  They don't know there are 90 degrees in a right angle, or that there are 12 inches in a foot.  They cannot multiply, or find basic square roots.  It takes them all twice as long to program problems into their fancy calculators than it does for me to do it with a pencil.  It is sad.  One girl I talked to said she'd NEVER been taught some of these things in high school.  She felt dumb. She's not dumb...how can she know what has never been taught?  

I'm so glad that I made my kids do math without the programmable calculators.  It is crippling people, mathematically.