Why do our schools rely on calculators and Indians have to use their brains?

[Deja Q]

http://blogs.techrepublic.com.com/programming-and-development/?p=396

Excerpt:

The person I was speaking with was a programmer visiting the U.S. from India. This gentleman and I had gotten to know each other fairly well, and he has been programming for quite some time, probably around as long as I have. He and I got onto the topic of education. It is a well-known fact that India, China, and a number of other countries are beating the U.S. in math scores. So I asked him how they teach math in India. He was almost baffled by the question, as if there was more than one way to learn math and this was the first time someone had let him know. “From a book, with examples on the blackboard, how else?” I queried him about the use of calculators and computers, two tools quite common in U.S. math education. He explained to me that calculators are forbidden in their version of high school and that, in colleges, the calculators allowed are basic models (think add, subtract, multiply, divide, exponents, square root, log 10, and natural log), and their usage even then is frowned upon to the point where using a calculator will be the cause of ridicule and humiliation. This sure sounded like a far cry from the educational environment in the U.S., where 7th grade students are now being required to own TI-85’s, a calculator that’s probably more powerful than the guidance system on a cruise missile.

(SNIP)

This is why the conversation with my Indian friend has me so worried. It seems to me that the schools in India, China, and many other countries are laying extremely high quality general education foundations for their students. I look at the “math” that my brother and sister learned (I am much older than they are), and I do not want to subject my child to the same kind of disastrous “education” (I am officially not a parent yet, but he is on his way in a few more days or weeks!). I love to see the best brought out in people. A mathematical foundation built upon computers and advanced calculators simply does not provide the basis to build a good programmer on.


So who is running our schools like they would a wal-mart?

More importantly, does all this suggest everything going on in the US is tokenism in terms of education?

The responses to the blog are also interesting reading.

[Name removed]

1. Deleted message

Message removed by moderator. Click here to review the message board rules.

[proud2BlibKansan]

7. Bullshit

Come do my job for one day and see how much fun you have teaching kids math.

I'd welcome you to DU but that seems kind of pointless.

[Beausoir]

44. Bullshit, indeed! I salute you!

The teachers are the first to get dumped on and it makes me angry.

[Dinger]

49. Yeah, Why Would Someone Do That? Why? Hmmmmmmm

I'll keep my thought private on THAT one.

[proud2BlibKansan]

88. First thing I thought of was

'is ATK related to BTK?' :scared:

BTK was that serial killer in Wichita. Odd screen name, don't ya think? LOL

[ATK]

98. it's an observation, not a condemnation

pdfio

[Dinger]

47. Thank You P2BL!

Sheesh! Boy, am I ever biting my tongue, HARD!

[ATK]

96. Math scores don't lie.

you might be the exception....but the statistics don't lie

[HiFructosePronSyrup]

123. Statistics don't lie?

:rofl:

[Name removed]

134. Deleted message

Message removed by moderator. Click here to review the message board rules.

[proud2BlibKansan]

147. What statistics?

[Deja Q]

8. I'm lucky. I got taught before calculators were mandatory.

If I can do what teachers can't, sign me up.

Or if the kids are so rude and violent and bully others and prefer to wear ribald t-shirts, lock them up.

[proud2BlibKansan]

9. I majored in Math and wish I could have learned to use a calculator in school

When I think of how much more Math I could have learned if we had calculators back in the dark ages when I was young . . .

[Horse with no Name]

64. Interesting point.

I grew up without calculators, my daughter grew up with them. She is a math genius. I am not. I can do the basic stuff in my head or on paper, but can't begin to grasp the more advanced stuff.
There are always two sides to every story and I do believe you have hit the proverbial nail on the head.

[proud2BlibKansan]

69. We go so much deeper in math now

It's amazing and wonderful how technology has improved the way we teach math.

I am also willing to bet your daughter used more manipulatives to learn math than you did.

[Horse with no Name]

78. What are manipulatives?

:shrug: I only passed Geometry because I played basketball.

[proud2BlibKansan]

79. Hands on objects

like counters, and pattern blocks and unit cubes.

[Horse with no Name]

81. It is what it sounds like then

I am a whiz at metrics--I wish we would go to those. Geometry, algebra, trig, etc...I struggle.

[proud2BlibKansan]

83. If you ever grabbed a handful of pennies

and gave them to your daughter to use as counters, you were using manipulatives.

When I taught 1st grade, one of my first homework assignments every year was for the kids to find manipulatives at home. That way they knew what they had on hand to use to help with their math homework.

[proud2BlibKansan]

82. Here is an article by one of my Math s/heroes on manipulatives

http://math.about.com/gi/dynamic/offsite.htm?zi=1/XJ/Ya&sdn=math&cdn=education&tm=7&f=00&tt=14&bt=0&bts=0&zu=http%3A//teacher.scholastic.com/lessonrepro/lessonplans/instructor/burns.htm

[Longhorn]

149. She's my hero, too!

I was lucky enough to get my training through alternative certification and we had some great workshops on manipulatives and calculators. I was a wiz at math all through college but I didn't really understand it well until I started this training. And I was in my forties! :)

[Greyskye]

126. Montessori manipulatives

It's really amazing to see what they do with math manipulatives in Montessori. Here is a snip to give folks unfamiliar with this a taste of what they do. It's pretty cool to see 3rd/4th graders figuring out square and cube roots using this stuff.

Math
The Montessori math program focuses on using concrete examples to illustrate abstract concepts, transferring quantities to symbols and learning the ones, tens, hundreds and thousands. Sandpaper numerals, number rods, cards and counters, teen and tens boards and a 1-100 board are all materials used to demonstrate the quantity to symbol recognition. Bank game and golden bead materials provide an introduction to the decimal system and basic operations. Squaring and cubing of numbers is demonstrated through the bead chains of varying colors.

[proud2BlibKansan]

148. Montessori has some amazing materials

but they are too darned expensive.

[ProfessorGAC]

71. Huh?

If you didn't internalize the concepts, then you learned NO MATH AT ALL! The calculator would not have helped you learn more. It cannot aid in the internalization of a mathematical concept. It only makes homework take less time.
The Professor

[proud2BlibKansan]

89. You didn't read my posts, did you?

:)

[TechBear_Seattle]

11. Same here

I was in college (as a math major) before I ever was allowed to use a calculator. And that was only because by the time you were doing advanced calculus, tests were on how to set up and solve problems, not on basic arithmetic.

[Deja Q]

12. Logical.

:thumbsup:

[proud2BlibKansan]

20. And the Math majors today have probably learned twice as much Math as you did.

[TechBear_Seattle]

30. Probably not

On what evidence to you base your claim?

I took 15 to 18 credits each semester. Six to 10 of those credits every semester were in either hard-core math classes as part of my major, or in heavily math-related coursework for my minor in physics; the remainder were for the general ed part of my degree and the occasional "sanity" class to give my right-brain a break. I find it unlikely that math majors only 14 years latter are learning more math than I did, and nonsensical that they are learning twice as much.

[proud2BlibKansan]

32. Well if you really are a math expert

then surely you understand that calculators allow much deeper and more intensive math learning.

Did you know we are now teaching algebra in elementary school? Thanks to calculators, we can move the kids into algebra much earlier than we used to.

[Johonny]

46. Got to agree

It'd be fun to watch people try to do complex climate modeling "in your head".

[HiFructosePronSyrup]

50. I disagree.

Calculators, and slide rules, and laptops (which people seem to put way too much emphasis on) are handy little tools for certain applications.

But they don't really help people learn, except how to use calculators, slide rules, and laptops.

[proud2BlibKansan]

59. Just like a computer allows you to write more and you don't have to spend time

using a dictionary, a calculator frees the learner up for more math.

You can't learn to use a calculator unless you understand the math you are programming it to do for you. I have been teaching kids to use calculators for years now and this is very true.

[HiFructosePronSyrup]

62. Calculators seem to free up time for chemistry, physics, etc.

I didn't take much college math, a year of calculus- derivatives, integrals, multivariable.

Than a course on linear algebra, and one on differential equations.

I don't remember using calculators. Probably because that was before calculators, but I don't remember many places where simple arithmatic and trig functions would have been handy.

Now solving simle math problems in fields other than math, then yeah. Clears up a hell of a lot of time.

[Longhorn]

154. Today's calculators do much more than simple arithmetic and trig functions.

You can instantly graph a function, determine its domain and range, view an accompanying table of values, find the zeros, minima and maxima, perform translations and transformations, graph a function with its inverse, find points of intersection between functions, solve systems of inequalities, etc. We generally don't teach doing these things INSTEAD of calculating by hand -- we teach the concepts with the calculator by demonstration and reinforce the algorithms. I advise my students (I teach and tutor at community college) to work the problem by hand and check their results with the calculator.

There are some concepts that are truly enhanced by graphing. For example, students are taught from as early as sixth grade how to solve a one-variable equation but many do not really understand how the "left side equals the right side." When we treat each "side" of the equation as a separate function, graph them, and find the point of intersection, we can actually demonstrate that there is one solution, no solution, or an infinite number of solutions.

The calculator also makes it easier to solve "real-life" problems that rarely have integer answers. One reason students don't "get" math is that we try to demonstrate its use with examples that no one would use algebra to solve because a simple "guess-and-check" approach makes more sense. Not every function is factorable, for example. Our problems involve functions that calculate how long it will take a car to stop at a certain speed or when it is safe to take a second dose of a drug or how deep light penetrates the ocean's surface -- functions whose coefficients are decimals or fractions and would be quite time-consuming to solve by hand. Students actually relate to these problems and gain confidence when they can solve them -- and confidence in math students is one of the biggest problems we as educators face. They're not stuck doing boring problems until they can handle the higher math.

[TechBear_Seattle]

52. As a math MAJOR, I disagree

First, I am a computer programming expert; that is what I do for a living and that is where I have received the most training. I studied a lot of math and got a degree, but that just makes me educated.

Second, teaching algebra (most likely, pre-algebra) in 6th grade isn't relevant. The concept of functional variability is useless when you do not know the basics; the problem with American teaching of mathematics is that the basics are being ignored. Kids no longer learn how to do math in their head, they no longer learn the properties of addition and multiplication, they no longer learn the difference between ratios and a division equation. By fourth grade, I knew that 1/2 = 2/4 = 3/6 just by looking at the ratio; today there are an appalling number of high school students who would have to pull out a calculator and actually punch in numbers before they could figure this out. By sixth grade, I could take any number and find its square root by using a pencil, a scrap of paper and basic logical reasoning. Today... I'd rather not think about it.

The mind is a muscle. It used to be that education was about training that muscle, getting it excercised and developed. Mathematics was a large part of that, as it taught not only something useful in and of itself, but also an entire toolset of logical processes and reasoning skills. Those skills are no longer being taught in American schools. Instead of teaching kids how to walk on their own, we put them in wheelchairs (ie give them a calculator) and pat ourselves on the back at how quickly they can move, never bothering to notice how their legs have become atrophied stumps. Calculators can be a valuable tool, yes. But using calculators before college level mathematics is not a tool, it is a crutch that results in permanent disability.

This is why science is failing: by the time people are studying geometry, trig and calculus, few kids have developed the ability to work things out on their own. A calculator is absolutely useless in proving the congruence of an angle or deriving the formula for the volume of a sphere or finding an equation to figure out how fast an oil spill is growing, and you can not teach in one semester of Euclidian geometry the skills needed to start learning Euclidean geometry.

I'm curious: why do you claim that calculators in elementary school are good? I've given my thoughts, please share yours.

[woo me with science]

56. Excellent, excellent post. Thank you!

I am always frustrated by the talking point arguments against teaching basic skills or rote facts in elementary school, on the basis that doing so prevents teachers from using that time to show children how to engage in "higher-level thinking and reasoning."

The basics and the rote facts are the raw material through which children can begin to make those higher level connections. Everything we know about cognitive science shows that children reach the higher levels of thinking by having the basics down so firmly and broadly that they can begin to manipulate/compare/apply that knowledge IN ORDER to make the next step and see the higher-level relationships and connections. It is true in math and history and every academic area.

The drive to leap to the "higher level" stuff first can be pernicious in math for exactly the reasons you describe. In history it can be just as pernicious. Absent a core knowledge of the FACTS underlying our history, "higher level" discussions about historical concepts can quickly become indoctrination, because the students don't have a fund of information from which to make connections, fact-check, and put into perspective what they are being taught.

[proud2BlibKansan]

66. And the mind is used differently today so different instruction and different

tools are necessary. We don't start algebra in 6th grade, we start it in 2nd and 3rd grade now. And calculators enable the kids to grasp fairly complex algebraic concepts we never used to teach until high school.

Like I have said repeatedly in this thread, if a kid doesn't understand basic math, he won't figure out how to use a calculator. It is not a substitute for learning arithmetic.

We do much more problem solving today. On one of our recent state Math tests for 4th graders, they were presented with a dinner for 100 people to plan. They had to figure out how much food they needed. All the food came in case lots and every type of food was in a different size case. They also had to calculate the cost of the dinner, and the value of the tickets sold. And the ticket prices varied from child to adult to family and pre-sale to day of event. Then they had to subtract the cost of the food from the ticket sales to get the profit. They also had to construct graphs to show much of their data. Sure they could have done all the arithmetic by hand to figure all this out but that would have taken a lot more time. So in one hour, using calculators, they did all this work.

Hopefully you have grasped that the objective of this exercise wasn't to show if they knew arithmetic, but rather to use their arithmetic and mathematics skills to solve a much more complicated problem than we would have given 4th graders even 10 years ago. Without calculators, we are back to teaching simple arithmetic. And surely if you are a parent, you want your children to know how to use their math skills in real life situations.

I really can't comment on your geometry remarks, since it has been years since I studied complex geometry and I have never taught it.

[TechBear_Seattle]

84. Minds are "used differently"?

:rofl:

You missed my point: mathematics is far, far more than just arithmetic. It is logic. It is reasoning. It is parsing a problem and finding a solution. It is examing a situation, picking out relevant information and using that information in a meaningful way. In the "old fashioned" way of teaching mathematics in grade school, these were part and parcel to learning arithmetic. When the teaching of arithmetic is bypassed in favor of reliance on calculators, the teaching of these skills -- necessary for real life, vital for any kind of work in science or engineering, and obligatory for anyone in a democracy -- is also bypassed.

Yes, kids might be learning concepts of algebra in 5th and 6th grade, but the fact is, they will be incapable of studying geometry, trigonometry, calculus, abstract algebra, discrete math, set theory or any other field of higher mathematics without extra study -- read time and money -- learning things they should have been given a chance to learn in grade school.

That a particular involved question was on a 4th grade test is meaningless; I had similar problems on standardized tests at the same grade. Comparing the percentage of students who got that set of questions correct last year and 25 years ago -- without using calculators -- would be relevant and very unlikely to be in your favor.

As for geometry, the usual first course class is two dimensional Euclidean geometry. You have two tools -- a "collapsable" compass to draw circles and a straight edge to draw lines -- a set of five postulates and a capacity for logical thought. Using this tiny toolbox, you prove various statements and then add those to the toolbox so you can prove other statements. It is in fact a course in rigorous logical which starts with skills that are normally learned in conjunction with arithmetic and which lays the foundation for all other higher math fields. If a student does not already have the starting skills, she will have to learn them before being able to start geometry with any hope of actually learning what it teaches.

[proud2BlibKansan]

87. Yes, we teach more complex problem solving and at an earlier age

And no, you did NOT have a problem like that on a 4th grade test unless you are just now around 20 years old. I collect textbooks. I can always check.

And yes, we do teach geometry, discrete math and many other higher level math areas in elementary school. Look up your state math standards. Most states have them listed online at their state dept of education website. Or you could just google "____ grade math standards (name of state)". I think you will be amazed by how math has changed for the better.

[TechBear_Seattle]

109. My experience says otherwise

Let's take the addition of 1048 and 296. The correct answer is only a small part of what is taught. The important part, the part that is eliminated when calculators are used, is how to take a large, complex problem and break it down into smaller, easier problems and solving those. Addition, subtraction, multiplication, division, exponents, roots... each technique of arithmetic requires different methods of reduction. A person must be able to master these methods before making further progress in mathematics. With calculators, students are not going to learn these methods no matter how vigorously they are taught.

I have looked at my state's math standards. The Washington Assesment of Student Learning (WASL) has been at the heart of public controversy for more than a decade and I, like many state residents, have looked at the requirements in depth. The assesment has three parts: reading, writing and mathematics. Of those three parts, the mathematics has received the most scrutiny. To quote from the Wikipedia article:

The WASL's mathematics section has received intense scrutiny. The Essential Academic Learning Requirements curriculum framework was based largely on the controversial NCTM standards which elevated content-independent problem solving and invented arithmetic methods over teaching one correct method to achieve one right answer, and even published papers by researchers such as Constance Kamii in their yearbooks advocating that teaching traditional arithmetic methods was harmful to learning.

The first set of sample problems published in 1997 for the 4th grade contained problems involving unusually advanced material, often taught in the 7th grade, including skills such as indirect measurement, similar triangles, proportionality, and independent probability. The WASL promotes the new standards-based mathematics, which often removes instruction of concepts such as carry, average, and long division in texts such as "Investigations", but adds median and mode, and requires drawing labeled pie charts from data. The goal stated by OSPI was to have 80% passing, yet in 1997 not even Somerset elementary, one of the very highest scoring elementary schools, met this goal. In some cases, the passing standard for all schools was set higher than the best schools. The Partnership For Learning claimed that the 10th grade WASL only requires 8th grade level math, but many samples require mastering algebra, a topic some students will not take until college.

As for grades, I have one word for you: inflation. Yes, more high school students today are getting better grades than high school students did 20 years ago. However, nearly twice as many of today's college freshmen are spending their first year of higher education in remedial math and writing classes than college freshmen of 20 years ago. And when high school seniors are given the very same standardized tests given to high school seniors 20 years ago, today's students score significantly below the previous generation.

The fact that advanced problems are being taught in the classroom and are appearing on standardized test is irrelevant. The fact that today's students are getting better grades than students of my generation is irrelevant. THE KIDS ARE NOT LEARNING THE MATERIAL AND THE PROOF IS IN THE RESULTS OF THE STANDARDIZED TESTS. I assert that this is because children are not being taught basic, necessary techniques and that calculators in early math education is a major reason why.

[proud2BlibKansan]

112. The standardized tests are not aligned with what is taught in most states

So they are not the best way to assess the kids. And they are not aligned because we don't have a national curriculum. We do however, have national standards which this article refers to as "controversial". Hmm I have been a member of NCTM for over 20 years and had no idea our standards were controversial. I will have to look into that.

In my state, our Math scores are fine. But we do have one of the better state assessment programs, written by our teachers. Our test is aligned with our state standards. We had a head start because we started our assessment program several years before NCLB was enacted. Under a great progressive Democratic governor, we were able to develop a model program long before most other states. Interestingly, however, NCLB requirements have caused us to change our test and it isn't as rigorous as it was before the feds stepped in and told us what kind of test we had to administer.

There is a key difference between your position and mine. You seem to focus on the tests, I am focusing on the kids. I know that standardized tests are one small piece of the assessment picture. And they are far from the best way to hold our kids and our schools accountable. You don't seem to realize that (and neither does our federal govt). Many gifted students do not perform well on standardized tests and many poor students score through the roof. If you really are a mathematician, then surely you can understand that on a multiple choice test, if there are 4 choices, the kids have a 25% chance of guessing and getting the right answer. I teach special ed and I can report that some of my students with mental retardation have scored higher on the fill in the bubble standardized tests than the gifted students. It isn't about the Math they know, it's about filling in the correct bubble.

My state had a very successful performance based assessment program but it did not meet the standardization requirements under NCLB. So now we give a fill in the bubble test that tells us nothing. Our old test was criterion referenced and gave us specific information about what each kid knew and did not know. We could actually use that test to plan instruction. Not any more. The federal govt also doesn't care about individual performance, they are only concerned with schools as a whole. We still give some criterion referenced performance items but the expense of meeting the federal mandate will eliminate that in a year or two.

Any educator will tell you a standardized test is not the best way to assess learning. It shouldn't be that hard for a mathematician to understand. It should also be obvious that No Child Left Behind is just a clever title for a law that really does not focus on what is best for kids. And educators tend to get fussy when govt officials forget about doing what is best for our kids.

[girl gone mad]

128. I took my son out of school a couple of years ago..

and started homeschooling. We were doing a lot of traveling and the state wouldn't allow for what they considered to be 'unexcused' absences.

In the beginning, I was taken aback by his poor problem solving abilities. He had always gotten straight A's in math so I assumed he was doing about the same as I had in school. Though he did well overall, he wasn't able to answer some simple problems without a significant amount of guidance.

The first thing I did was make him memorize a multiplication table backward and forward. I couldn't believe he'd made it trough elementary school without having it burned into his brain. Then we reviewed all of the basic properties, discussed classical principles and went from there. My son is now doing college level calculus and geometry. It's amazing how fast kids can learn when they have a solid understanding of the fundamentals. It's so important to really understand mathematical ideas, not just to interpret them.

My Relativity professor used to tell me he could teach relativity to elementary school students. Their minds are open to new concepts and even a theory as advanced as Relativity rests on just a few fundamental notions.

Mathematicians are lazy, in a sense, since they generally seek out the simplest means of solving a problem. Calculators are simply a tool. A lack of basic understanding, as you pointed out, appears to be the problem. I don't know that calculators cause this lack of understanding, since I also had to teach my son how to properly use one. In my opinion, there is too much hand-holding going on. Kids are shown exactly what to do, step by step, instead of being encouraged to figure things out in a more natural way.

[Tesha]

151. I have complete confidence that...

> By sixth grade, I could take any number and find its square
> root by using a pencil, a scrap of paper and basic logical
> reasoning. Today... I'd rather not think about it.

I have complete confidence that you really still do remember
how to take a square root using Newton's method (pick an
arbitrary divisor, average the divisor and the quotient,
lather, rinse, repeat until it's accurate enough for your
taste.)

Now synthetic division you may not remember; heck, I'm not
sure I ever understood it in the first place and given
the existence of slide rules (and later, scientific
calculators), there was no need to understand a more-
optimized method of hand-calculating a square root.

Tesha

[ToeBot]

57. Algebra is taught when students are able to conceptualize variability

It's question of mental age not grade level. The use or non-use of a calculator is irrelevant.

[proud2BlibKansan]

70. I am merely pointing out that math instruction is very different today

and calculators are just one change. Algebra in elementary school would be another difference.

[ProfessorGAC]

74. Sorry.

That's not logical. As i said above, the calculator is not a way to internalize a concept. It's just a faster tool. Geting the math done faster doesn't make it more internalized. You, me, or anyone else here would not have had a deeper understanding of mathematics if we used calculators.

That just flies in the face of learning theory and modalities. You should know better.
The Professor

[proud2BlibKansan]

76. Well I do know better and here is why:

27 years of teaching Math in elementary school. Before and after calculators. The Math we teach today is much more complex.

[TechBear_Seattle]

111. That what is being taught is more complex is not at all relevant

What are the students LEARNING? Do the standardized tests show that students are actually learning? And what follow-up studies have shown that students who take this "more complex" math in elementary school are able to use these skills latter on, in high school and college?

From what I have seen in Washington, the answers are very clear. Students are not learning, the standardized tests show this, and studies have shown that more and more college freshman are having to take remedial math before they can take standard, college level courses.

[proud2BlibKansan]

113. The standardized tests merely show that kids can fill in bubbles,

the right bubbles. And it compares how well they fill in bubbles with how well all the kids their age filled in bubbles on the same test. On one day out of an entire year. A performance based assessment system would be a much better way of knowing what our kids have learned.

When the standardized test scores for my kids come in, I file them away and never look at them. They tell me nothing in terms of what I need to teach them, what they already know and what they need to learn. They merely reflect a wasted day my kids spent filling in bubbles on a scantron sheet.

[TechBear_Seattle]

114. So by what can you say that students are learning?

If the standardized tests are meaningless, why do you hold them up as "proof" that students are learning this material (as you did with the example of planning a complex dinner that was on a standardized test)?

What is the metric you are using to measure student learning? You keep dodging this very basic question, no matter how I ask it.

[HiFructosePronSyrup]

116. How do you know the students are learning?

You ask the teacher. If you don't want to interact with teachers, and apparently a lot of people don't, luckily they send home a report card.

[proud2BlibKansan]

122. It's not that simple

This is one of those issues that has been analyzed to death and it's impossible to come up with one pat answer that fits all schools and all kids.

If you are asking my professional opinion, I would prefer a portfolio based assessment program where kids are monitored at regular intervals all throughout the school year. In my state, we have grade level expectations in each subject area and we had explored assessing each of those over the course of a year and using that as an assessment tool. We were still working on the logistics of that when NCLB invaded our world.

In special ed, we used to administer individual achievement tests that gave us diagnostic and prescriptive data in each subject for each of our kids. We could use those test results to write IEPs and plan instruction for the year. We no longer administer those tests, since our kids with disabilities are required to take the same fill in the bubble tests the non disabled kids take. I would prefer returning to the better achievement tests for our special ed kids, but this is not practical for all students.

In my perfect world, every state is allowed to set its own standards and every school district is free to meet those standards in the best interest of their kids. Local control is the best and most effective model for education. Let each community rate its own schools. And most importantly, return those billions of dollars in federal education funding that never leave DC to the local school districts. The money being wasted on administrative expenses under NCLB is shameful.

[frankenforpres]

77. i minored in math

no calculators used for Calc 1,2,3


for computational stuff, we use Matlab, or Maple.

[Dinger]

51. Hit And Run Posts Are So Frustrating nt

[treestar]

132. That's a gross overgeneralization

And why is it so now when it wasn't in previous generations? Are you saying Indian teaching colleges are better, too? So why don't we send our potential teachers there?

[AlinPA]

2. Years ago, we used a slide rule in college and some thought that was "too easy"

[hobbit709]

3. It was always faster doing it in my head

than trying to work a slide rule.

[HiFructosePronSyrup]

4. Yes, let's go back to slide rules.

That'll be useful.

Damn kids these days don't even know how to work one.

[cloudbase]

117. I went through college engineering back in the slide rule days.

Because you had to keep track of powers and decimal placement in your head, you had a better connection to the numbers and would have some sense of whether your computed answer was in the ballpark or not. Today, people tend to accept whatever answer the calculator spits out, even if they've made an input error, without any sense that the answer may not be quite right. Hell, if the cash register didn't tell the cashier how much change to give, I doubt that many would be able to figure it out on their own.

[Tesha]

153. Slide rules were useful because...

Slide rules were useful because they actually illustrated
some useful principles as you did your arithmetic on them.
Addition and subtraction of logarithms, multiplication of
logarithms, the continuity of the trigonometric curves,
etc.

You also had to develop an intuitive understanding of
orders of magnitude ('cause the slide rule didn't calculate
those for you).

Tesha

[TahitiNut]

22. I miss my K&E Log Log Duplex Decitrig.

:evilgrin:

[cloudbase]

119. I've still got mine!

Same model. I remember getting a piece of advice: If you're going to study engineering, buy the best slide rule you can, because you'll be using it all your professional life.

[TahitiNut]

125. Yup. Us true nerds carried it in its holster clipped to our belt. (Wearing pegged chinos.)

I can't even remember what happened to it ... after nearly 50 years.

[NewJeffCT]

5. In China, elementary school students are required to have laptops

It's all about how you use them. If you still focus on the required skills, then I think using a computer or calculator is fine.

Being an accountant, people used to complain that being allowed to use a calculator on the CPA exam actually made the test harder because they added more into the test to compensate for the faster computing time.

Edited to add that the requirement for laptops in China is more in the wealthier eastern sections of the country (which still has more people than the entire US)

[proud2BlibKansan]

6. First of all, it is not valid statistically to compare our kids to kids in other countries

There are too many differences. Not only on the test, but culturally. Unless the Indians, Chinese, and these "many other countries" test the same cross section of kids (they don't) and give them the same test (they don't) these comparisons are not valid. It's apples and oranges. Anyone who ever took an introductory statistics class should understand that.

This is a false and nasty right wing talking point. It is disheartening to see it here on this progressive message board.

Yes, our schools are failing. But not because we give our kids calculators. Ask any mathematician. A good understanding of math and number sense is vital to even understand how to work a calculator.

No our schools are failing because the right wing wants them to fail. NCLB is accelerating that failure. If you really are concerned about this, instead of criticizing schools with false talking points, lobby for the elimination of NCLB.

[Deja Q]

10. So asking questions is a bad thing?

That's why I post a lot of what I do.

Blanking H. Blank, the number of people who otherwise call me naive, few should be surprised I ask questions.

Or am I supposed to toe a line, asking questions and having free will being a sin?

Damn straight I am concerned. Which is why I ASKED and post REFERENCES to the SOURCE MATERIAL. Is that a crime? Sentence me to condine action, come to my place and shoot me in the skull and spare you my misery known as curiosity.

I also won't be accused of being called a freeper. (Ironic, since they seem to toe a line and on their board have no tolerance for people who ask questions later... to keep you from guessing, I had an account on there once too.)



I will also ask - will you sign up to techrepublic and speak to the person whose article I linked to, and sort him straight?

[proud2BlibKansan]

14. Haven't we had this discussion before?

Forgive me if I am confusing you for a DUer who likes to criticize public education.

And I did answer your question. No, we cannot say that the kids in India are more advanced in Math than the kids in the USA. Since we have yet to fairly compare our kids to their kids, we have no way of knowing who really is better in Math. I am inclined to think our kids would smoke their Indian peers under the table if they really don't teach their kids to use calculators in India. You see, kids can learn much more advanced Math if they know how to use a calculator.

I also find it hard to believe they don't use calculators in India. But looks like this is just an anecdotal story and we all know how reliable those are. :eyes:

[HiFructosePronSyrup]

18. You were asking questions?

I could have sworn you already had all the answers.

[Dinger]

60. Thank You (Again):

"This is a false and nasty right wing talking point"

[Horse with no Name]

67. I actually think that sports kills academics in schools

I believe THAT is the difference between our country and others.

[Rage for Order]

73. Then why did schools fail prior to NCLB?

NCLB has only been around for a few years, but our public schools have been in trouble far longer than that. It isn't some "vast right wing conspiracy" that's causing a breakdown in public education. While there are national standards, the vast majority of public school policy is made at the local level by local school boards, not by politicians in the back rooms of Washington DC, so unless the town itself is right wing, chances are it's not right wingers setting up the schools to fail. There are a number of reasons for the decline, but in my opinion one of the biggest problems is that schools and parents are more concerned with not harming a child's self esteem than they are with actually making sure they learn something. Witness the move away from using red ink to mark incorrect answers or make notes on papers as one small example of this trend. Red ink is just so harsh and has negative connotations, so we mustn't use it. Better to use purple instead lest we hurt little Johnny's feelings.

[proud2BlibKansan]

85. They really didn't fail

And they were (always have been) grossly underfunded.

Everyone laughs about the red pen thing, but there is actual research behind that. I have never used red pens to correct. I hated seeing all those red marks when I was in school and I have always tried to remember what it was like to be a student. I remembered one of the better teachers I had used a green pen. So I never did use red. Then about 10 years ago, research came out that explained exactly why red was so bad. It sends a negative message to the brain. Mistakes are very important; we learn from them. If we approach a mistake with a negative attitude, we are less likely to correct it accurately.

[Rage for Order]

90. Well, some failed, some didn't

The same as it is now - some schools are failing, some aren't. And is it so bad that a student receives a negative message when they are wrong? The red ink thing was one minor example, but there are a number of others, such as the movement in some communities to stop keeping score at children's sporting events, allowing seniors to walk in their graduation when they haven't satisfactorily completed all of the course work just so they won't be embarrased or feel bad, parents not supporting their child's school in disciplinary matters (because their child would NEVER do something like that!), lack of parental involvement in their child's education, etc.

I don't think lack of funding is the issue in most schools. Washington DC spends more per pupil than any other state in the country, yet DC has some of the worst public schools in the country (yes, I know DC isn't a state, but it's clssified as such for the purpose of tracking spending per pupil).

[proud2BlibKansan]

97. Per pupil spending varies widely even with a school district

because some kids cost more to teach than others. Take 2 kindergarteners. One comes from a 2 parent home, stay at home mom, was read to every day (probably several times a day), has been to the zoo a jillion times, went to pre-school at the best Montessori school in town, has health insurance and regular dental check ups. The other one has a single parent who works 40+ hours a week at a minimum wage job, has no health insurance, has never been to a dentist, Mom has no time to take him to the zoo and is too tired to read to him when she gets home; he is in a crowded day care until he starts kindergarten, and Mom can't afford pre-school.

Which child will cost more to teach?

And before anyone says it, yes, private schools have lower per pupil costs because they have lower expenses. They pay their teachers less, generally don't have transportation expenses and the parents do a lot of fund raising. And yes, they generally (but not always) have better test scores because they can pick and choose which kids to admit, while a public school has to take every kid who walks in the door. Private schools can kick kids out when they don't perform up to standard; public schools cannot.

So no, you can't compare per pupil spending and get an accurate picture. It's much more complicated than that.

[ProfessorGAC]

75. Proper Techniques Can Compensate For Those Differences

So, it can be made statistically valid. And, i'd bet many social statisticians have already developed the algorithms. I'll see at least one this weekend. I'll check.
The Professor

[proud2BlibKansan]

92. Then you need to write a book

This is one of those perpetual problems statisticians have been trying to solve for years.

[july302001]

143. No.

Comparison of academic performance on a subject that is studied worldwide (math) is not automatically a "right wing talking point."

It's a valid point that may impact whether India supplies our engineers 15 years down the road, or whether we Americans get a shot at these good jobs, for a decent wage.

[proud2BlibKansan]

146. The reason it's a rw talking point

It's an invalid comparison. In other words, it's bullshit. Yet the rw brings it out to "prove" that our American public schools are ineffective. That way, they build support for the vouchers they so desperately want.

Like I said before, until we test the kids in 2 different countries with the same test under the same circumstances, (and it would help to compare kids from similar socioeconomic backgrounds), we are comparing apples and oranges. That is invalid.

[BlooInBloo]

13. Because American teachers and students are stupid?

[proud2BlibKansan]

16. Bingo!

May as well stop funding public schools then and let parents use vouchers to send their kids to school anywhere they want. :sarcasm:

[BlooInBloo]

23. If one infers stupidly, then yes...

... There is an alternative, however.

[mainer]

15. The real reason India and China are ahead: NO SPORTS!!!

I am getting crabbier and crabbier about this topic. I see how much energy and money and parental attention goes into school football and basketball teams. Raise money for new football uniforms! Try out for cheering squad! Practice dribbling and shooting baskets every day after school! Drive your kids here and there, all day and every day, to this meet and that meet.

In the meantime, funds for school orchestras and libraries and arts are being cut.

When I was growing up, every public school had an orchestra. Kids learned to read music and play instruments. In Japan, learning music is now required, because they've found it enhances math scores. In one study in American inner-city schools, half the kids were assigned music classes in which they had to learn to read music and play an instrument, while the other half didn't get music class. The kids who learned music did better in EVERY OTHER CLASS. In other words, just learning to read music lifts the student's achievement in other areas.

Now it's hard to find a single public school here in Maine that has an orchestra. Yet 30 years ago, many of them did. We've gone backwards.

And I think it's because Americans are so stupidly sports crazy.

It translates to city politics as well. In San Diego, they raised millions and millions of dollars to build a new stadium. And cut the city library's funds.

[proud2BlibKansan]

21. I am wondering how much time Indian kids spend

playing video games instead of doing homework.

[TahitiNut]

25. The worst thing about the 'sports' programs in our schools (imho) is ....

... they don't focus on life-long sports - and they attract only those who are already adept. (That's not 'teaching,' that's 'harvesting.') The tennis and golf programs are the closest they get and good luck finding viable programs for those in the blue collar schools.

[mainer]

26. Sports teams are "elitist" -- not everyone can participate

A lot of money goes toward high school varsity teams that are, by definition, elitist because they only choose the best athletes. So the nerds in schools are subsidizing the jocks -- and the nerds can't take part.

[TahitiNut]

40. That point deserves emphasis. What if they didn't allow kids take a course unless they got an 'A'?

The idea that only the kids who're already adept at some sport get to participate is (imho) antithetical to what an education is all about. While I graduated back in 1961, I don't see much of a change.

If there are two things we need in our schools, it's true mental health education (including critical thinking, counselling, and logic) and true physical health education (which should include life-long activities). I'd love to see schools teach Tai Chi and Yoga. I'd love to see schools teach kids how to enjoy using their bodies - how to move, how to enjoy it, and how to make the most of their own body mechanics. While I think it's an improvement that soccer has been added to the sports, it's really not enough. We need to train people in those physical activities that are individually available in our communities. We tend to focus on activities that support various commercial industries - equipment manufacturers and professional leagues - and not what's actually beneficial over a person's lifetime. We're making them consumers, not participants.

[HiFructosePronSyrup]

45. AP classes.

Supposedly for the elite students.

[rinsd]

93. And Honors classes. And Gifted and Talented programs (nt)

[rinsd]

95. Elitist? LOL. Is the band elitist for only taking people who can play?

Are honors/AP classes elitist for choosing who is allowed to take them?

"A lot of money goes toward high school varsity teams that are, by definition, elitist because they only choose the best athletes."

I am speechless. While a varsity team would compose the elite players for the given sport, it is not elitist. Being elitist is believing that one's participation on the team makes one more relevant, important etc.

"So the nerds in schools are subsidizing the jocks -- and the nerds can't take part."

LOL. Yes all that bakesale money for uniforms. Those bastards!

[mainer]

99. Anyone can learn to play music.

Which means ANYONE can join the school band. It's democratic, based only on focus and desire.

But there's a limited number of slots for the basketball team or the football team. And the little kid who can't make the "cut" is left out.

Athletes are blessed with good genes and bodies. And athletics gets the lion's share of money. How much does, say, the chess team or the science team get?

[rinsd]

102. "How much does, say, the chess team or the science team get?"

How much do athletics get?

"Anyone can learn to play music."

Really? As someone who has tried his hand at violin, trumpet, percussion, tuba and piano I beg to differ.

"Which means ANYONE can join the school band. It's democratic, based only on focus and desire."

How is the school band democratic? Do you vote on what to play?

I would suggest more time on the books and less time in the band at this point. You seem to have a tenous grasp on the actual meaning of terms like democratic and elitist.

[mainer]

103. See meaning #2 for "Democratic"

If you're going to start insulting people for their use of language:

dem·o·crat·ic Pronunciation Key - Show IPA Pronunciation
–adjective
1. pertaining to or of the nature of democracy or a democracy.
2. pertaining to or characterized by the principle of political or social equality for all: democratic treatment.
3. advocating or upholding democracy.
4. (initial capital letter) Politics.
a. of, pertaining to, or characteristic of the Democratic party.
b. of, pertaining to, or belonging to the Democratic-Republican party.

Yes, democratic also means "social equality for all; "democratic" treatment.

(That you would think it ONLY means "people always get to vote" is pretty funny.)

In the context I used it, is correct.

As for "more time on the books," I make my living as a writer, with a background in science. I'm not a musician. But even I can see that the mania of sports in this country has caused it to lose quite a few IQ points.

[rinsd]

104. The school band isn't about social equality. It is simply an open membership

Or are you unfamiliar with the concept of 1st chair?

"As for "more time on the books," I make my living as a writer, with a background in science. I'm not a musician. But even I can see that the mania of sports in this country has caused it to lose quite a few IQ points."

One could say such a view is elitist.

[mainer]

106. yep, I'm elitist. I believe that education's superior to brute force

and I also believe that the average IQ of people watching a game in a football stadium is probably lower than the average IQ of people watching an orchestral performance.

whether I'm right or not will have to be tested.

[rinsd]

108. That's the problem with black and white thinking.

You look at it as either/or when there is plenty of room for both.

Athletics aren't interfering with academics. Stupid No Child Left Behind is doing that. Its not the football team's fault that there are fewer science classes.

You also ignore the positive benefits of athletics, the most basic of which is regular exercise to say nothing of learning about working with others towards a goal, self esteem etc.

The impact of athletics on women in particular is amazing.

[HiFructosePronSyrup]

124. Wow.

How eurocentric.

[AngryAmish]

31. India and China are not ahead of us

By any reasonable and objective standard we are a more advanced society and have a standard of living much higher than India and China.

Why do millions of college aged people try to come to the US for college and not the other way around? Because of our superior education system.

You like music. We are happy for you. However if you can show me cutting music in education has cratered the IQ of students as a whole in the US then I will believe you. Oh, wait, you can't? That pesky Flynn Effect continues apace? Then I guess music didn't help that much.

[mainer]

34. The objective data we're using is student math scores

There's the data. We're not talking about who's a more "advanced society". We're talking about TESTABLE, OBJECTIVE data. And that is school math scores.

As for the link between music education and school achievement tests, I cited one study below. There are other studies in the neurological literature.

Yes, there are studies. What do yo have against music education?

[mainer]

37. from the Washington Post: U.S. math scores lag behind other countries

http://www.washingtonpost.com/wp-dyn/content/article/2006/10/17/AR2006101701298.html

[proud2BlibKansan]

72. What Angry Amish said

[AngryAmish]

41. We test everyone, they don't

Feeble minded children do not even get into school there.

on edit: I have nothing against music education and intend to have my children learn music. That said, this one note song about the evil of sports gets old.

[Neoma]

35. In a sense, sports are welcome.

Think of how many kids get little exercise these days. They just need to work it out through something different other than sports maybe.

[mainer]

39. We need physical education -- but not sports team mania

California required 1 hour of physical activity every day when I was growing up. That's great. But nowadays, sports have spilled into every single free hour of a kid's time, and all they're doing after school and all weekend is running around a soccer field, to the detriment of any learning activity.

I've spoken to parents who are EXHAUSTED from attending the games of their multiple children. Families miss mealtimes together, they miss family vacations, they spend all their time on the road driving to games all over the state.

When those kids grow up, how many of them will still be playing football or basketball? How much difference will it make to their lives when they're forty or fifty?

In the meantime, the kid who's learned a new mental skill will most likely be using it for the rest of their lives.

[july302001]

144. problems existed 30 years ago as well

I agree here. Sports has gone too far both at the school and college levels. Also, the schools are too focused on letting the kids socialize that they don't emphasize academics.

The problems with American students' math performance didn't start yesterday. I'm against calculators before 8th grade (kids need to memorize their times table and need to know how to do long division), but think they're OK for high school level courses.

I was shortchanged by my school system during the 1970s and early 1980s. I got straight A's in school, but college calculus was like hitting a brick wall. I would have gladly majored in engineering but for my difficulty with calculus.

My school system was hit by the Prop. 13 funding crisis in California and also had deteriorating discipline.

[toddaa]

17. Arithmetic and Math are two different beasts

A TI-85 will do graphing of derivatives and trig functions, but I'll be damned if it will write proofs.

[napi21]

19. I remember being considered a really mean mother when my kids

were in grade school and I said NO CALCULATORS, even though most of the other kids had them. I told them, once they learned how to do the math and understand exactly what they were doing, I'd buy them a calculator, but not before!

They're both grown now and have kids of their own. Both are very good in math, and have used the same phylosophy with their kids. Only one of the grandkids is old enough for me to tell, but she is doing GREAT, even plays SODUKO (sp) for fun.

I disagree with the way our schools are teaching today, but parents can do support training at home and improve their children's learning a lot!

[mainer]

24. Study shows: musicians end up smarter than athletes

So why do we keep emphasizing sports over the arts? It only makes Americans STUPID.

"Musicians did score higher than the athletes did, and over time this gap widened. Findings indicate that factors other than enrollment in a performing music class were affecting the outcome. The schools represented in this study reflected a cross section of different types of music programs. Results also indicated an overall drop in standardized test scores in the ninth grade that was not seen for student musicians."

http://eric.ed.gov:80/ERICWebPortal/custom/portlets/recordDetails/detailmini.jsp?_nfpb=true&_&ERICExtSearch_SearchValue_0=ED448186&ERICExtSearch_SearchType_0=eric_accno&accno=ED448186

[HiFructosePronSyrup]

27. Yes, but what about drummers?

[mainer]

28. I think they may be in the same sad category as accordion players

only kidding!

The studies I've seen were only about keyboard and string players. I've seen no data on drummers.

[proud2BlibKansan]

29. Drummers are musicians.

[tkmorris]

94. Hey ya bastid

Drummers aren't stupid, they are just........ different.

[frankenforpres]

80. selection bias -nt

[mainer]

101. Nope. One study split up a school randomly into music and non-music

Inner city school. Students split randomly. Half got keyboard music lessons, the other half got computer keyboard lessons.

Music students did better in every subject.

Not selection bias in this case.

[porphyrian]

33. Everyone cares about education until it's time to fund it.

And then, they're more likely to get metal detectors than they are books or decent teachers. So, we get stuck with the most expedient method of proving they can force knowledge into our stupid kids in the most efficient way possible on almost no money - standardized testing. That way, they have plenty of official-looking statistics to help people who probably haven't been within sight of a public school in decades unless they gave a speech there decide where they can cut even more money from education.

The state of our public education is a reflection of our level of concern with it.

[LeftishBrit]

130. Never was a truer word spoken!

[porphyrian]

131. It's one of my most oft-repeated rants. I've had a chance to clean it up.

;)

[SheilaT]

36. I have taken advanced math

-- through to first semester or so of calculus before and after calculators. When I was in h.s. forty plus years ago, no one dreamed we'd have graphing calculators. Doing quadratic equations was extremely tedious. You'd have to plot multiple points to begin to be able to graph it. And most of the points you'd find were actually only approximations, because doing it with pencil and paper could not give you precise numbers out to five decimal places much of the time.

Then I came back to math after more than thirty years. I tested in to 2nd year algebra, which is pretty impressive. (I had a wonderful math course in high school no one has ever heard of.) And then the teacher showed us stuff on the graphing calculator. Oh, my! It was possible to solve problems, to find the exact precise points, to see just how small changes in one of the values of a quadratic equation shifted the entire thing. Wow! I'd plot quadratics endlessly, because it was so interesting to see them. Before, plotting each one would be about a 15 minute exercise. Who's going to do ten of those just for fun?

Yeah, the basics do need to be taught. Kids need to learn their times tables. (By the way, I went to a school that didn't bother with them past nine times, and I wasn't terribly handicapped by that). And it's somewhat useful to memorize squares of numbers up to some point.

Every time I see these kinds of silly debates about how calculators are ruining our children, I remember that ancient Greeks actually pissed and moaned about literacy, LITERACY for pete's sake because that meant kids wouldn't memorize the epic poems. Well, now that I don't have to spend a major part of my life and brain capacity memorizing The Iliad, I can instead read every new translation that comes out, and consider -- or maybe even discuss with others -- the relative merits of a prose versus a poem translation.

[Jim__]

38. I'm not sure I agree with the article.

This seems particularly questionable: A mathematical foundation built upon computers and advanced calculators simply does not provide the basis to build a good programmer on.

I agree that if our kids aren't learning arithmetic because all the computing is done for them on calculators, that's a problem. But, if they know basic arithmetic, and they know how to use calculators to help in solving complex problems, then, I think that's a great education. The best way to learn programming is to program; so, it seems like a pretty good foundation.

I don't believe that a mathematical foundation can be built upon computers and calculators. I'm not sure what the author is seeing.

[durrrty libby]

42. In grade school and High School my youngest did not do that

well nor care that much about math. He did enough to get by

Now he is a 3rd year engineering student

Statistics,trig, geometry, calculus,physics. He loves them all.


Some professors let them use calculators and some don't

He is successful because he is self-motivated and he really enjoys

his instructors

He has a full load this summer and sometimes up all night


preparing for the next day's class. His chem class is 16 hours per week for 12 weeks

and Dr B is enormously fussy. My son does not mumble and grumble. He just does the work

Anyone can get a great education in this country, but they have to want it and put forth the effort.

[JCMach1]

43. Better check the modern Indian curriculum... they do use calculators and other tools...

There is little focus on creativity and parents virtually browbeat (or literally beat) their children into overstudying for their examinations. It is largely rote learning and doesn't pay much respect to critical thinking.

Sorry, but I teach many students who come out of this system... American students are much stronger in creativity and critical thinking skills.

[NewJeffCT]

54. Same with China

I had posted above about how students in the wealthier eastern part of China ("only" about 400 million or so people) are required to have laptops by around the 4th grade. It is a lot of memorization and rote learning (I think the whole writing system is learned mostly through memorization)

Our educational system has its problems and needs improvements, but I bet our top students beat the top students in India and China most of the time.

[girl gone mad]

133. The parents that come here often behave the same way.

I have known Indian children who were hit and screamed at by their parents for getting math problems wrong.

[Sequoia]

48. Congrats on your upcoming baby!

[Dinger]

53. I Anticipate That This Thread Will Get Locked

And it should if this kind of crap continues, IMO.

1. Attacks on teachers (I've seen this before, at DU,of all places) :
" Because our teachers can'tteach our kids how to do math"
" Because American teachers and students are stupid?"
. . . . nice, real nice
2. Pro-voucher posts
3. Anti-public school posts
4? I can't wait to see some more posts like I've seen so far. Sickening.

[Name removed]

55. Deleted message

Message removed by moderator. Click here to review the message board rules.

[SayWhatYo]

58. Well that would be upsetting.

Yes, lock everything that a subset of people disagree with... Oh wait, then everything will be locked.

Btw, from what I saw, the pro-vocuher posts were sarcasm.

[Dinger]

61. So What

Many a "true" word is said in jest.

[LoZoccolo]

100. Lame.

Try defending your own point of view.

[Horse with no Name]

63. I never used a calculator in school growing up

They taught us in the first grade how to use "counters". When given the option, I STILL prefer to figure things myself instead of using calculators.

[Skidmore]

65. Our teachers started cutting corners when parents started whining

about Johnny and Jane having too much homework and not enough time to hang out with their buddies. Heavens to Betsy, we wouldn't want the little darlings to have to study now, would we?

[durrrty libby]

105. The other day there was a thread discussing pre-K and a

parent of a 4 year old was complaining that nowadays

kindergarten is a "pressure-cooker" I kid you not.:eyes:

[La Lioness Priyanka]

68. first your level of obsession with indians is weird, secondly a calculation use is efficient.

having studied in both countries i support Americas' use of calculators.
\

[Dinger]

86. Thank You lionesspriyanka

:) I appreciate it.

[La Lioness Priyanka]

107. these thread about india taking away american jobs are however tedious

control your own corporations and government. stop blaming foreigners and maybe we'll still have a fighting chance, you know?

[rinsd]

91. I was in HS in the early 90's. Only time a calculator was needed was for Trig (nt)

[donco6]

110. I just hate these threads.

Yeah, we can't teach math. No one is learning math here. There are no engineers being trained anywhere. No math majors in college. We all suck. Let's just all go and die.

Bleh. I'm too tired after a long school year to even argue with this stupidity.

[MissB]

115. You know what really sucks about US math?

We still teach predominantly in the English units. What a PITA to convert (in your head) to the Metric system.

Meh on the calculators. I don't think that has much to do with math scores. I'd say that Americans in general value intelligence much less than they do physical prowess or questionable musical ability.

[BlooInBloo]

118. All of my physics classes from over a decade ago at a small state school were metric.

[MissB]

120. All my engineering classes a little more than a decade ago were

dual. The instructors switched back and forth, and the textbooks presented both units. Why? Because we should have been learning in metric, but because nearly all of us were products of the US public educational system, we knew English units like the back of our hand.

My kids, attending arguably the best public school in the state, are being taught math predominantly as I was in elementary school - in English units. Yes, metric units are introduced, but later.

Absolutely fucking backwards as hell.

[slowry]

121. Why Johnny Can't Add

(the book, written by Morris Kline, is freely available http://www.marco-learningsystems.com/pages/kline/johnny/johnny1.html">online btw)

Let us look into a modern mathematics classroom. The teacher asks, "Why is 2 + 3 = 3 + 2?"

Unhesitatingly the students reply, "Because both equal 5"

No, reproves the teacher, the correct answer is because the commutative law of addition holds. Her next question is, Why is 9 + 2 = 11?

Again the students respond at once: "9 and 1 are 10 and 1 more is 11."

"Wrong," the teacher exclaims. "The correct answer is that by the definition of 2,

9 + 2 = 9 + (1 + 1).

But because the associative law of addition holds,

9+(1+1)=(9+1)+1.

Now 9 + 1 is 10 by the definition of 10 and 10 + 1 is 11 by the definition of 11."

Evidently the class is not doing too well and so the teacher tries a simpler question. "Is 7 a number?" Thà students, taken aback by the simplicity of the question, hardly deem it necessary to answer; but the sheer habit of obedìence causes them to reply affirmatively. The teacher is aghast. "If I asked you who you are, what would you say?"

The students are now wary of replying, but one more courageous youngster does do so: "I am Robert Sinith."

The teacher looks incredulous and says chidingly, "You mean that you are the name Robert Smith? Of course not. You are a person and your name is Robert Smith. Now let us get back to my original question: Is 7 a number? 0f course notl It is the name of a number. 5 + 2, 6 + 1, and 8 - 1 are names for the same number. The symbol 7 is a numeral for the number.

The teacher sees that the students do not appreciate the distinction and so she tries another tack. "Is the number 3 half of the number 8?" she asks. Then she answers her own question: "Of course not! But the numeral 3 is half of the numeral 8, the right half."

The students are now bursting to ask, "What then is a number?" However, they are so discouraged by the wrong answers they have given that they no longer have the heart to voice the question. This is extremely fortunate for the teacher, because to explain what a number really is would be beyond her capacity and certainly beyond the capacity of the students to understand it. And so thereafter the students are careful to say that 7 is a numeral, not a number. Just what a number is they never find out.

[BlooInBloo]

127. Nothing worse than idiots doing philosophy.

[proud2BlibKansan]

137. That is complete crap and not at all how we teach Math

[slowry]

140. Sure ok

It was written in the 70s, so maybe the example doesn't ring as true today as then, but it illustrates a very real and current problem in mathematics education.

[proud2BlibKansan]

141. No it doesn't

It's an overblown example of an ineffective lesson. Plus we don't teach Math at all the way we did in the 70s.

[slowry]

142. that was never 5 minutes n/t

[LeftishBrit]

129. There is a huge amount of argument in the UK as well about the use of calculators in schools...

Some think they ruin mathematical skills; others that they are a liberator. In fact, considering the intensity of the debate, actual studies suggest that the use of calculators as such has relatively little effect, one way or the other, on mathematical skills; though the *ways* in which they're used in teaching has a bit more of an effect.


Most studies of the effects of calculator use have shown few strong effects in either direction on arithmetical calculation or reasoning than might be expected. A meta-analysis of over 80 studies (Hembree and Dessart, 1992) indicated that calculator use had little effect on the development of arithmetical computation skills. Problem-solving was better when pupils used calculators than when they did not. Experience with calculators had no effect, or a weak positive effect, on problem solving when calculators were not available.

Hembree and Dessart's study, and others on calculator use, can be found in: J. Fey and C. Hirsch (eds.) Calculators in Mathematics Education; National Council of Teachers of Mathematics, 1992.

As for cultural and international differences in mathematics, they seem to have lots of causes: social attitudes to mathematics; country's economic status and funding of education; level of children's involvement in cultural practices, such as buying and selling, that involve number; amount of time spent on mathematics at school; level and nature of teachers' own education in mathematics; amount of opportunity for discussion of mathematical strategies; even features of the language: for example, Chinese has a more regular counting system than English.

One very interesting book about international differences in teaching practices is: L. Ma: Knowing and Teaching Elementary Mathematics: Teachers' Understanding of Mathematics in China and the US; Erlbaum, 1999. Another interesting book about cultural influences in mathematics, and how the same children may perform very differently in different contexts, is T. Nunes, A.D. Schliemann and D.W. Carraher: Street Mathematics and School Mathematics; Cambridge University Press, 1993.

For the general topic of mathematical thinking, a good book is Brian Butterworth: The Mathematical Brain; Oxford University Press, 1999 (I think the book is published in America as "Everybody Counts").

[Longhorn]

135. It is false that 7th-graders are required to have a TI-85.

First, that's not even the latest model -- if they were going to require a calculator of that level, it would be a TI-86. Second, even in high school, it's a TI-83 or 84 that is required -- a graphing calculator. And what it allows students to do is quickly graph a function, determine its zeros or minimum or maximum, etc. It's a TEACHING tool allowing students to see the effect of changing the leading coefficient or slope or other transformations. There is a table function that helps students make a numerical connection in addition to the graphics. Middle school students also learn algebra -- they will be able to use a TI-83 or 84 all the way through college.

I teach math at a community college, everything from basic math to precalculus, and I tutor in our tutoring center and do private tutoring. A calculator doesn't replace thinking -- it enhances it. A student couldn't even use the calculator without some understanding of the mathematics. Functions don't always come ready to enter (that is, solved for "y".) In order to set the proper viewing window, a student has to have some understanding of domain and range. And teachers, knowing that students are using the calculator, include problems on tests that cannot be solved with a calculator or require them to solve "by hand" and show all steps.

I was tutoring an Algebra II student last night and we were doing a half-life problem that, by hand, can only be solved with logarithms. We did it by hand and then I showed him how to solve it with the graphing calculator (he would have had to use the calculator to get the final answer anyway -- I can't imagine anyone advocating for going back to multiplying and dividing multi-digit numbers, even if you used a table to find the logs! What a waste of time!) In determining how to set the window so that we could see the zero of the function, we had to discuss a reasonable estimate of the answer -- something that a student who was doing the problem by hand wouldn't even have to consider. This meant that he had to understand that we were solving for time and not just a variable. You can advise a student to check the "reasonableness" of an answer but to solve with a graphing calculator, it is often a necessity.

I teach both methods interchangeably in order to reinforce the concepts. The students who use a calculator seem to have a better overall understanding while those who don't get so bogged down in arithmetic that they often give up before they get to the "breakthrough."

I once taught eighth grade next to a woman who told her students that the calculator is "the devil's tool." She was a fundie in every sense of the word. She was also a walking calculator -- a wiz at number sense. She could multiply and divide multi-digit numbers in her head in seconds. Yet, at a workshop we both attended, she seriously asked the facilitator, "Why do we have to use this 'f-of-x' notation? Why can't we just use "y"? She had a minor in mathematics and a framed sliderule on her wall. :shrug:

[proud2BlibKansan]

138. Thank you for your terrific response!

:)

[july302001]

145. interesting post

Interesting post.

[BlooInBloo]

150. "everything from basic math to precalculus" - wow. What range.

[Longhorn]

155. I have a masters in math education.

These are the classes I've been assigned to teach at a community college that only teaches through differential equations. Frankly, without further study, I don't feel qualified to teach beyond Cal II. Does this somehow negate my training, experience, and opinion? :shrug:

[BlooInBloo]

156. Yup.

[BlooInBloo]

152. "we were doing a half-life problem that, by hand, can only be solved with logarithms." - LOL!

[Nikki Stone1]

136. It's called the Service Economy. Real industry requires real brains

And real industry has been leaving the US since the 1970s. We are being left with an economy that will require workers to operate machines and be nice to people. The real thinking (and the jobs that require it) has been outsourced.

[gravity]

139. Calculators are more efficient

Instead of wasting our time calculating trivial problems, we can focus more of our energy focusing on greater challenges.

If India has there own philosophy that harder is always better, than that's there problem, and America will still remain number one in technological innovation. The only advantage Asia has on us at the moment is costs.