Carpe Diem

More on ‘reform math’ as a failed educational exercise in replacing what works with what sounds good

Scary: Only 57% of college freshman could solve the simple division problem above (231 / 7 = 33) without a calculator (using old-fashioned long division) based on a math assessment test given by Professor Cliff Mass in his Atmospheric Sciences 101 class at the University of Washington.

Here’s a hint why – according to a math teacher quoted in the NY Times, “We don’t teach long division…. it stifles students’ creativity.” Here’s more from the 2006 NY Times article “As Math Scores Lag, a New Push for the Basics:

For the second time in a generation, education officials are rethinking the teaching of math in American schools.

The changes are being driven by students’ lagging performance on international tests and mathematicians’ warnings that more than a decade of so-called reform math — critics call it fuzzy math — has crippled students with its de-emphasizing of basic drills and memorization in favor of allowing children to find their own ways to solve problems.

Across the nation, the reconsideration of what should be taught and how has been accelerated by a report in September by the National Council of Teachers of Mathematics, the nation’s leading group of math teachers.

It was a report from this same group in 1989 that influenced a generation of teachers to let children explore their own solutions to problems, write and draw pictures about math, and use tools like the calculator at the same time they learn algorithms.

But this fall, the group changed course, recommending a tighter focus on basic math skills and an end to “mile wide, inch deep” state standards that force schools to teach dozens of math topics in each grade. In fourth grade, for example, the report recommends that the curriculum should center on the “quick recall” of multiplication and division, the area of two-dimensional shapes and an understanding of decimals.

Grass-roots groups in many cities are agitating for a return to basics. Many point to California’s standards as a good model: the state adopted reform math in the early 1990s but largely rejected it near the end of the decade, a turnaround that led to rising math achievement.

The frenzy has been prompted in part by the growing awareness that, at a time of increasing globalization, the math skills of children in the United States simply do not measure up: American eighth-graders lag far behind those from Singapore, South Korea, Hong Kong, Taiwan, Japan and elsewhere on the Trends in International Mathematics and Science Study, an international test.

See a video demonstration here of some “rainforest math,” and you’ll get a good idea why it’s being abandoned,  in favor of a return to math basics.

See previous CD posts on reform/rainforest math here, here and here.

81 thoughts on “More on ‘reform math’ as a failed educational exercise in replacing what works with what sounds good

  1. You’re going to loose a lot of kids who grew up on leap-pad math technology while potty training if you stand at a board and draw numbers on it and tell them to memorize them. That would a great test to see how many students you could keep awake. You can’t teach ‘em if you don’t reach ‘em :)

    • Of course you have never used educational material on a computer have you? We have found programs on line fthat basically do the flash cards and spelling quizzes the way we used to – cuz it works and the kids get a little fun reward at the end. So why would parents be clamoring to find the old methods online when the new ones work so well.

      The really thing is that in my day my mother didn’t have to worry about my learning in school. Now you have to watch everything and eventually go to homeschooling.

      Note too in the 1970s there were already special programs for kids who were having trouble. They went an hour a day for private sessions.with a specialist. I had to go for a week even because I missed a month of school in first grade and they wanted to make sure I caught up.

  2. Of course this leads to a story by Isaac Asimov, in the future no one does arithmetic except by calculator or computer, all have forgotten how. Then one day someone discovers the by hand way. The real question is with ubiquitious calculators, (most cell phones seem to have one now), does one really need to know how to do long division in particular should it be taught before algebra? Or would it be better to teach compound interest theory, since many don’t understand this, and of course the infamous rule of 72 used to figure out interest on installment loans. (I recall having an office mate who had a question about pay off and the person on the other end said you would have to be a mathmetician to understand this, and he said but I have a PhD in math.

  3. One of the best pieces of advice I got in a math class is to learn how numbers relate, rather than trying to memorize stuff.

    Math is not my strong suit. I’m good with stats (mostly because it’s what I do for work and in my daily baseball life). I can do percents and I can estimate percent changes quite well.

    But trig, calculus? Forget about it.

    Anyway, the teacher taught me a different way of thinking about numbers and functions. Rather than memorizing rules, he had me learn relationships. That way, even if I were to use a calculator or Excel or something, I could tell right away whether or not the answer was right. After all, even a calculator is only as smart as the operator.

    After he taught me this, my math improved. Now that I knew the relations, I could tell when an answer was wrong, retrace my steps, and figure out where I went wrong. this skill I was lacking before.

    I tell this story because I think maybe we shouldn’t rush to judgement about this Rainforest math. Maybe something unconventional is the way to go.

    • This is probably true in about 5th grade. You still had to – or should have memorized addition and multiplication tables in First and Third grade. That is when we learned tricks.to do math.

      Helping kids out with difficulties wasn’t invented last year as some here seem to claim.

      • Well, like how 9 relates to 3 (9 is 3*3, or 3^2). How multiplying something by 9 works.

        basically getting a “feel” for the numbers.

        I know that’s nebulous, but it’s hard to explain.

          • Yes Jon, you learn how numbers relate and then memorize X tables for simple and effective efficiency.

            I don’t need to ask myself “why” after I understand why. I want understanding and then efficiency thereafter.

        • Jon

          Well, like how 9 relates to 3 (9 is 3*3, or 3^2). How multiplying something by 9 works.

          basically getting a “feel” for the numbers.

          Gotcha, and I agree. With that type of understanding the mechanics become easier.

  4. neither old math nor new math are likely to fix the problem because the world has changed and the basic problem is US schools that’s not a problem in OECD schools – is that we do not teach real world problem solving/critical thinking using math – and science – as well as language (to understand real world technology scenarios).

    we do not teach critical thinking and it’s starting to show up in other ways – like a distrust of science and scientists, belief in creationism, and disbelief in evidence-based work and reliance on “beliefs” instead.

    THe rest of the OECD world is pointed right at the 21st century global job/employment world and we are hating life and our college-graduating kids are working in the only thing they truly qualify for – service industry jobs.

    we blame our education system but instead of looking at what OECD is doing – we want to revert….

    • “we blame our education system but instead of looking at what OECD is doing – we want to revert….”

      I blame the parents first. You know, baby daddy and baby mama.

      “our college-graduating kids are working in the only thing they truly qualify for – service industry jobs.”

      It’s a free country but pul-eeze know that if you graduate in majors that have a demand one can a get great job in the USA.

      Larry, you are engaging in hyperbole but I will stop because I find your comments “useful”.

      • Cit

        It’s a free country but pul-eeze know that if you graduate in majors that have a demand one can a get great job in the USA.

        I can attest to that. My degree in axe grinding has prepared me for a great job that only requires me to work part time, so I am able to attend all the local rallies and protest the 1%.

      • re: ” “we blame our education system but instead of looking at what OECD is doing – we want to revert….”

        I blame the parents first. You know, baby daddy and baby mama.

        I agree and both themselves have terrible educations so there is no culture of education in the house.

        “our college-graduating kids are working in the only thing they truly qualify for – service industry jobs.”

        It’s a free country but pul-eeze know that if you graduate in majors that have a demand one can a get great job in the USA.

        Yes.. I AGREE AGAIN! but we have high tech jobs that go begging and/or end up with employees with foreign surnames while many of us don’t have enough of the right kind of education to get those jobs.

        Our parents, schools and kids shy away from robust academic subjects like math these days. They get the minimum required and that will not get you the better jobs..

        I worked in an environment where mathematicians worked with programmers to develop orbital models which requires two strong disciplines – the pure knowledge of math at a high enough level to write equations to represent launch and orbital flight and the ability to encode them in simulation and fire control systems.

        Neither job was one you get by getting minimum math in high school and college – and that was years ago and now we’re doing autonomous vehicles which adds even more complexity to math and software.

        Larry, you are engaging in hyperbole but I will stop because I find your comments “useful”.

        okay. but IMHO it’s _not_ “hyperbole” to want to see the US become a better competitor for global jobs and to educate others so that they can at least get a job, support their family, help their kids with school, instead of needing entitlements, getting incarcerated and breeding yet another cycle of dependent people.

        Education is the key. the best economies in the world have highly educated workforces and we did not advance with them but fell behind and it ought not to
        be a big secret… that leads us to wrong conclusions like “going back to basics”.

        If we are serious about the problem – we need to ditch the ideology and either mimic what the OECD countries are doing or develop alternative ways that are globally competitive – not insular.

        we have to “own” the problem or else no matter how much you help you kids – your kids will then grow up to pay entitlements for the kids that did not get effective help because they had ‘bad parents’, etc.

        If we really care about “the kids” – we need to recognize that if we do not change – we will continue in future generations what we are doing now – and thats a fail.

        • Please name a single country that fits your criteria of “the best economies in the world have highly educated workforces and we did not advance with them but fell behind and it ought not to be a big secret.” Here’s a list of countries by GDP PPP per capita, the US places around 6-8, ie in the top 10. Please tell me which one of Qatar, Brunei, or Monaco is more “highly educated” than the US and therefore advanced past us.

          Which OECD country is it that is more educated and therefore so advanced? Germany, at 20% below our GDP PPP per capita? The UK, France, or Japan, all at 30% below? Norway, where 10% of the economy is from oil, not to mention 30% of govt revenue? Which is it?

          • re: ” Please name a single country that fits your criteria of “the best economies in the world have highly educated workforces and we did not advance with them but fell behind and it ought not to be a big secret.” Here’s a list of countries by GDP PPP per capita, the US places around 6-8, ie in the top 10. Please tell me which one of Qatar, Brunei, or Monaco is more “highly educated” than the US and therefore advanced past us.”

            You can easily verify which countries are the highest educated by looking at PISA testing results:

            http://en.wikipedia.org/wiki/Programme_for_International_Student_Assessment

            then if you look at the countries that outrank us – virtually all of them are OECD countries.

            “Which OECD country is it that is more educated and therefore so advanced? Germany, at 20% below our GDP PPP per capita? The UK, France, or Japan, all at 30% below? Norway, where 10% of the economy is from oil, not to mention 30% of govt revenue? Which is it?”

            in your list of PPP countries – what I call the most advanced economies in the world – are OECD and virtually all OECD countries outrank us academically.

            but what we are advocating in this country educationally is to go back to 1950 style academics and that’s where many 3rd world and developing world countries are right now – and they have ever lower academic performance that us or OECD and weaker economies.

            I’m okay with us going in a different direction in academics as long as we measure results and the results prove it’s better than our competitors.

            I’m opposed to adopting other methods and refusing to measure.

            Many of the good jobs in this country are being taken by people with foreign surnames – because – we do not have enough sufficiently educated to take those jobs so we lose them to foreign emigrants.

            but on a worldwide basis – we are failing worse. If we cannot even outcompete foreign immigrants in our own country, you know we’re know attracting companies here than need highly educated workforces.. and we’re losing those companies to countries that do have highly educated workforces.

            We are still the tops – but we are starting to lose ground to others because we lag in our educational attainment compared to our competitors.

          • re: ” Please name a single country that fits your criteria of “the best economies in the world have highly educated workforces and we did not advance with them but fell behind and it ought not to be a big secret.” Here’s a list of countries by GDP PPP per capita, the US places around 6-8, ie in the top 10. Please tell me which one of Qatar, Brunei, or Monaco is more “highly educated” than the US and therefore advanced past us.”

            You can easily verify which countries are the highest educated by looking at PISA testing results:

            en.wikipedia.org/wiki/Programme_for_International_Student_Assessment

            OK, so which one does better than us economically “and we did not advance with them but fell behind?”

            then if you look at the countries that outrank us – virtually all of them are OECD countries.

            Nobody cares if they outrank us on some stupid test results. You claimed their economies had benefited, yet somehow they are all significantly poorer than us.

            “Which OECD country is it that is more educated and therefore so advanced? Germany, at 20% below our GDP PPP per capita? The UK, France, or Japan, all at 30% below? Norway, where 10% of the economy is from oil, not to mention 30% of govt revenue? Which is it?”

            in your list of PPP countries – what I call the most advanced economies in the world – are OECD and virtually all OECD countries outrank us academically.

            Yet, all their economies are not “advanced,” as almost all are poorer than Alabama. Do you consider Alabama “advanced?” You claimed that “we did not advance with” the “best economies,” yet they are considerably behind us.

            but what we are advocating in this country educationally is to go back to 1950 style academics and that’s where many 3rd world and developing world countries are right now – and they have ever lower academic performance that us or OECD and weaker economies.

            But your beloved OECD economies also do much worse than us, despite doing better on your tests. Gee, I wonder if education isn’t the reason then, but their much heavier govt involvement choking off their economies?

            I’m okay with us going in a different direction in academics as long as we measure results and the results prove it’s better than our competitors.

            I’m opposed to adopting other methods and refusing to measure.

            This would be okay if you knew what to measure. But since you and other testing advocates have no idea what is worth measuring or whether the idea even makes any sense, it is a horrible idea to standardize on your tests.

            Many of the good jobs in this country are being taken by people with foreign surnames – because – we do not have enough sufficiently educated to take those jobs so we lose them to foreign emigrants.

            No, those countries have populations of hundreds of millions or even billions, so their most talented come here to live better lives. You can’t compete with the most talented people from every other country, no matter how hard you try by pumping even more money into our broken school system.

            but on a worldwide basis – we are failing worse. If we cannot even outcompete foreign immigrants in our own country, you know we’re know attracting companies here than need highly educated workforces.. and we’re losing those companies to countries that do have highly educated workforces.

            Which companies are we “losing?” Is there a Google that was started in some other country? An Apple? A Microsoft? If you mean that these US companies are hiring abroad, I refer you to my previous paragraph. There is no need to “outcompete foreign immigrants,” we bring them here because they are the best for the job and may be willing to work cheaper.

            We are still the tops – but we are starting to lose ground to others because we lag in our educational attainment compared to our competitors.

            Ah, I see, so that was complete nonsense earlier about how “the best economies in the world have highly educated workforces and we did not advance with them but fell behind.” After all, how could we still be “the tops” if “we did not advance with them but fell behind?” :)

            The problem is not “educational attainment,” it’s big government. I don’t know how you can read this blog day after day and not get this.

          • re: ” Please name a single country that fits your criteria
            en.wikipedia.org/wiki/Programme_for_International_Student_Assessment

            OK, so which one does better than us economically “and we did not advance with them but fell behind?”

            then if you look at the countries that outrank us – virtually all of them are OECD countries.

            Nobody cares if they outrank us on some stupid test results. You claimed their economies had benefited, yet somehow they are all significantly poorer than us.

            they are more economically advanced that countries will lower academic performance – except for us – right now but the fact that they outperform us academically does not bode well for the future – especially when have have jobs here that are not being filled by our own citizens but by foreign born people.

            if this trend continues, we will start to see economic changes and this is NOT ME saying this. THis is quite a few American corporate leaders saying this, companies like GOOGLE, Microsoft, Oracle, etc.

            Yet, all their economies are not “advanced,” as almost all are poorer than Alabama. Do you consider Alabama “advanced?” You claimed that “we did not advance with” the “best economies,” yet they are considerably behind us.

            can you provide data that shows they are poorer than Alabama? All of their people have better education and better health care than us so how are they “poorer” ?

            “but what we are advocating in this country educationally is to go back to 1950 style academics and that’s where many 3rd world and developing world countries are right now – and they have ever lower academic performance that us or OECD and weaker economies.

            But your beloved OECD economies also do much worse than us, despite doing better on your tests. Gee, I wonder if education isn’t the reason then, but their much heavier govt involvement choking off their economies?

            then in that case the NON-OECD countries should do better by your reasoning, right? why don’t the non OECD countries outperform the OECD countries?

            I’m okay with us going in a different direction in

            This would be okay if you knew what to measure. But since you and other testing advocates have no idea what is worth measuring or whether the idea even makes any sense, it is a horrible idea to standardize on your tests.

            I’m OKAY with those who want to FIND OUT what to measure – two in particular seem to be math/science literacy and critical thinking in using math/technology to solve real world problems.

            but you have to want to know… instead of denying it.

            Many of the good jobs in this country are being taken by people with foreign surnames –

            No, those countries have populations of hundreds of millions or even billions, so their most talented come here to live better lives.

            that’s not what our own tech companies are saying

            You can’t compete with the most talented people from every other country, no matter how hard you try by pumping even more money into our broken school system.

            I agree.. but if you deny that what the OECD is doing, do you really have a serious alternative? what is it?

            but on a worldwide basis – we are failing worse. If we cannot even outcompete foreign immigrants in our own country, you know we’re know attracting companies here than need highly educated workforces.. and we’re losing those companies to countries that do have highly educated workforces.

            Which companies are we “losing?” Is there a Google that was started in some other country? An Apple? A Microsoft? If you mean that these US companies are hiring abroad, I refer you to my previous paragraph.

            yes.. we are “outsourcing”… and most companies now days are multi-national and have choices where to find employees.

            There is no need to “outcompete foreign immigrants,” we bring them here because they are the best for the job and may be willing to work cheaper.

            We are still the tops – but we are starting to lose ground to others because we lag in our educational attainment compared to our competitors.

            Ah, I see, so that was complete nonsense earlier about how “the best economies in the world have highly educated workforces and we did not advance with them but fell behind.” After all, how could we still be “the tops” if “we did not advance with them but fell behind?” :)

            the lag time but we are starting to see more and more Americans who do not have the educations needed to work in high tech companies – and the subject of this blog gets into that problem – our college graduates are not even good at BASIC math, much less advanced math.

            The problem is not “educational attainment,” it’s big government. I don’t know how you can read this blog day after day and not get this.

            I DO READ IT but it has contradictions.

            the countries with the least govt have the worst educational attainment and economies yet the ideologues here insist that we should model our country after 3rd world countries in terms of govt.

            it does not “compute”.

            I keep asking for a list of the countries with the least government that top us in education, literacy and economy and it’s hand-waved away…

            Name the best countries with the least govt and better literacy and economies than the countries with the most govt.

      • I blame the parents first. You know, baby daddy and baby mama.

        Why? The government makes you pay for their crappy education system, whether or not you want it, at the same time they incentivize less well off people to get divorced and not get married in the first place. The welfare system is truly an evil system.

        People respond to incentives in all things, including family structure.

        • Ken, yes the guvmint does incentivize idiotic choices. But, if one truly is concerned for their offspring, they wait to have children after education and saving some, as well as teaming with a like minded mate — the incentives are there to move up the economic ladder and do right by the children if baby mama and daddy make good choices.

    • neither old math nor new math

      There is no “old” and “new” math (1+1 = 2 is as true today as it was 10,000 years ago), merely approaches to teaching it. The new method is a proven failure, while the old is a proven success.

      is that we do not teach real world problem solving/critical thinking using math

      This is false. The problem is trying to get kids to solve real world problems using tools they don’t understand. Using technology, as you suggest, doens’t increase people’s understanding. When I taught college statistics, I can tell you one of the main problems with my students is their over reliance on using technology, rather than working through the problem.

      Saying the problem is not enough use of technology is like saying for a Olympic lifter to get stronger, they should use technology that will let them lift more weight. But who thinks that using a fork lift will make a person’s body strong? The same is true for claiming that a person’s mind will get strong if they just use enough technology.

      we do not teach critical thinking

      That’s largely right. Many in the educational system have embraced the “more technology” paradigm, rather than focusing on critical thinking.

      a distrust of science and scientists

      The politicization of science and scientists is an excellent reason to distrust science and scientists. The food pyramid, the vaccination=autism scandal, and AGW pseudoscience rely on “belief” far more than emperical data and all have caused much harm to the average person.

      In addition to this corruption of science, scientists are just people, too, prone to mistakes as often as the next guy. To simply take the word of a scientist because he’s a scientist, is the exact train of thought that the people you clearly dislike take: relgious people.

      our college-graduating kids are working in the only thing they truly qualify for – service industry jobs

      Why is this bad? The highest paying jobs in the US are service industry jobs, like sales, engineering, computer science, doctors, nurses, and law.

      our college-graduating kids are working in the only thing they truly qualify for – service industry jobs

      Because the OECD are largely not good examples of anything other than being largely subsidized by the US. Not going in that direction, reverting back to more free market solutions, is exactly what we should be doing.

      • neither old math nor new math

        There is no “old” and “new” math (1+1 = 2 is as true today as it was 10,000 years ago), merely approaches to teaching it. The new method is a proven failure, while the old is a proven success.

        and how do the OECD methods compare?

        is that we do not teach real world problem solving/critical thinking using math

        This is false. The problem is trying to get kids to solve real world problems using tools they don’t understand.”

        is that true of OECD kids?

        “Using technology, as you suggest, doens’t increase people’s understanding. When I taught college statistics, I can tell you one of the main problems with my students is their over reliance on using technology, rather than working through the problem.”

        I’m not advocating the use of technology. I’m saying that understanding math and understanding current technologies is needed to seek 21st century jobs in technology.

        “Saying the problem is not enough use of technology is like saying for a Olympic lifter to get stronger, they should use technology that will let them lift more weight. But who thinks that using a fork lift will make a person’s body strong? The same is true for claiming that a person’s mind will get strong if they just use enough technology.”

        I’m not saying the use of technology. I’m saying understanding it – being able to understand it in terms of being able to function as a worker in developing technology.

        “we do not teach critical thinking

        That’s largely right. Many in the educational system have embraced the “more technology” paradigm, rather than focusing on critical thinking.”

        GAWD we AGREE! my experience in high school and college is that HS and College avoid “word” problems like the plague because the kids simply do not have a good enough understanding of the math they have learned to actually USE IT to solve real world problems.

        and I saw this in my own work where only people with “B” or better averages in Mathematics BS were hired because they had to understand how to use the math
        in computer modelling.

        “a distrust of science and scientists

        The politicization of science and scientists is an excellent reason to distrust science and scientists. The food pyramid, the vaccination=autism scandal, and AGW pseudoscience rely on “belief” far more than emperical data and all have caused much harm to the average person.”

        there is a LOT of “science” though and it seems to me that only certain small areas are experiencing “distrust” on the scale we are seeing.

        some of this I attribute to “arm chair” / sound-bite understanding of how science works.

        the same people who build computer models for hurricanes can create other models for climate – and none of them are ever perfect.

        there can be 30 different hurricane models and none of them predict the exact path and yet no one accuses them of corrupt science. why?

        “In addition to this corruption of science, scientists are just people, too, prone to mistakes as often as the next guy. To simply take the word of a scientist because he’s a scientist, is the exact train of thought that the people you clearly dislike take: relgious people.”

        I agree. That’s why you what peer-reviewed science and a strong – wide – consensus – and even then with a grain of salt sometimes but that’s a HEALTHY distrust not an unhealthy one.

        “our college-graduating kids are working in the only thing they truly qualify for – service industry jobs

        Why is this bad? The highest paying jobs in the US are service industry jobs, like sales, engineering, computer science, doctors, nurses, and law.”

        a good number of service industry jobs are NOT good if you have a college degree in theory for higher level work.
        SOME are good paying. Many are not and it’s not enough to raise a family and save for a house and retirement.

        our college-graduating kids are working in the only thing they truly qualify for – service industry jobs

        Because the OECD are largely not good examples of anything other than being largely subsidized by the US. Not going in that direction, reverting back to more free market solutions, is exactly what we should be doing.

        I hear that but I disagree unless you can explain how reverting back is not headed back towards 3rd world free markets.

        What I hear is an advocacy for something – that does not exist so far on earth.

        It’s a country with 3rd-world level govt involvement but OECD world economies.

        I’ve yet to see that combination … only higher level economies associated with higher level government and lower level economies associated with crummy economies.

        are there real world examples of less govt and better economies?

        • and how do the OECD methods compare?

          What methods are they using?

          I’m not saying the use of technology. I’m saying understanding it

          Really? You want to teach kids the inner workings of a calculator or computer? Do you really think this is easier than teaching math?

          Do you not know that to understand technology, you have to understand math as a prerequisite?

          my experience in high school and college is that HS and College avoid “word” problems like the plague

          My experience in high school was the over use of completely irrelevant word problems. If Joey leaves Philly at 2pm travelling… blah blah blah. Not relevant and mind killing. No train rider does this. These contrived word problems are the horrific end of the drive to come up with “real world problems”. They are mind killing and not helpful in any way. That’s why they are the butt of jokes, rather than well respected educational methodologies.

          there is a LOT of “science” though and it seems to me that only certain small areas are experiencing “distrust” on the scale we are seeing.

          Largely those areas highly politicized, like AWG, that have very contradictory empirics, but are surrounded by politicians, and their scientist lackeys, claiming “the science is settled”.

          the same people who build computer models for hurricanes can create other models for climate – and none of them are ever perfect.

          Or even close to reality. The observed climate contradicts the models. Now those politicized scientists are saying “who you gonna believe, our models or reality”, expecting people to believe their models. The non-linearity of the PDEs surrounding climate models are poorly understood by everyone, including the scientists (the Navier-Stokes equations remain a millenial problem, i.e., a mystery, despite two centuries of scrutiny).

          “peer-reviewed science”

          Peer-reviewed science has been shown, repeatedly, to not be very peer-reviewed, and in fact very full of holes.

          a good number of service industry jobs are NOT good if you have a college degree

          This is an argument to make higher education market based, this way people don’t get bamboozled into studying irrelevant twaddle, like getting a master’s degree in puppetry. Subsidizing such foolishness is just that: foolish. This is also an argument against many people going to college. Wasting time and money on some credential that yields no benefits is a drain on society. Why encourage it?

          I hear that but I disagree unless you can explain how reverting back is not headed back towards 3rd world free markets.

          Jesus, Larry, “3rd world free markets”? Seriously? Third world countries are anything but examples of free markets. These places are third world because they don’t have free markets. The governments there are places that simply take from their citizens to support their own lavish lifestyles at the expense of citizens. In other words, they are the opposite of free markets.

          What I hear is an advocacy for something – that does not exist so far on earth.

          Slave owners said the same thing to abolitionists. Using the police state to take from others to fund your pet projects, just because everyone else is doing it, really is one of the weakest arguments the left brings forth.

          It’s a country with 3rd-world level govt involvement but OECD world economies.

          What are you talking about?

          are there real world examples of less govt and better economies?

          Literally hundreds, which you have been provided over and over for years on this website, but you never believe them. There are many examples in America’s past where the pressures of government shrank, resulting in a huge boom (notably the 1960s and the 1980s), while a metastasizing government crushed the life out of the economy (like the 1930s and what’s happened in the last ten years).

          • and how do the OECD methods compare?

            What methods are they using?

            I’m not saying the use of technology. I’m saying understanding it

            Really? You want to teach kids the inner workings of a calculator or computer? Do you really think this is easier than teaching math?’

            they have to understand math and language before they can understand technology and yes they do need to learn about how BASIC technology works.

            If you give a middle school class a project to build a robot – they have to be ABLE to read and understand the technologies needed to build it.

            “Do you not know that to understand technology, you have to understand math as a prerequisite?”

            yup.

            my experience in high school and college is that HS and College avoid “word” problems like the plague

            My experience in high school was the over use of completely irrelevant word problems. If Joey leaves Philly at 2pm travelling… blah blah blah. Not relevant and mind killing. No train rider does this. These contrived word problems are the horrific end of the drive to come up with “real world problems”. They are mind killing and not helpful in any way. That’s why they are the butt of jokes, rather than well respected educational methodologies.

            the word problems are the beginning of the rigor that is needed to use math and science to understand and articulate how things do work and to use that to go further.

            if you go to work in an organization that creates computer models for moving vehicles – you will need to understand those “word” problems and then some. These are the kinds of problems that the OECD kids beat ours.

            “there is a LOT of “science” though and it seems to me that only certain small areas are experiencing “distrust” on the scale we are seeing.

            Largely those areas highly politicized, like AWG, that have very contradictory empirics, but are surrounded by politicians, and their scientist lackeys, claiming “the science is settled”. ”

            why not other science? like cancer or tsunamis or asteroid orbits?

            the same people who build computer models for hurricanes can create other models for climate – and none of them are ever perfect.

            Or even close to reality. The observed climate contradicts the models. Now those politicized scientists are saying “who you gonna believe, our models or reality”, expecting people to believe their models. The non-linearity of the PDEs surrounding climate models are poorly understood by everyone, including the scientists (the Navier-Stokes equations remain a millenial problem, i.e., a mystery, despite two centuries of scrutiny).

            but you’re ignoring the hurricane modelling question here.

            they’re not even close to reality either but we don’t accuse them of bad science. why not?

            “peer-reviewed science”

            Peer-reviewed science has been shown, repeatedly, to not be very peer-reviewed, and in fact very full of holes.

            it’s not perfect and can be corrupted – no question – but it’s a HELL of a lot better of arm chair science “beliefs”.

            “a good number of service industry jobs are NOT good if you have a college degree

            This is an argument to make higher education market based, this way people don’t get bamboozled into studying irrelevant twaddle, like getting a master’s degree in puppetry. Subsidizing such foolishness is just that: foolish. This is also an argument against many people going to college. Wasting time and money on some credential that yields no benefits is a drain on society. Why encourage it?”

            I agree. I don’t think college loans should be available unless the intended degree is in a field that needs degreed graduates.

            I hear that but I disagree unless you can explain how reverting back is not headed back towards 3rd world free markets.

            Jesus, Larry, “3rd world free markets”? Seriously? Third world countries are anything but examples of free markets. These places are third world because they don’t have free markets. The governments there are places that simply take from their citizens to support their own lavish lifestyles at the expense of citizens. In other words, they are the opposite of free markets.

            okay – so give me examples of what you ARE advocating.

            “What I hear is an advocacy for something – that does not exist so far on earth.

            Slave owners said the same thing to abolitionists. Using the police state to take from others to fund your pet projects, just because everyone else is doing it, really is one of the weakest arguments the left brings forth.”

            it’s not left or right guy. I’m asking you for some examples of what you’re advocating for.

            It’s a country with 3rd-world level govt involvement but OECD world economies.

            What are you talking about?

            are there real world examples of less govt and better economies?

            “Literally hundreds, which you have been provided over and over for years on this website, but you never believe them. There are many examples in America’s past where the pressures of government shrank, resulting in a huge boom (notably the 1960s and the 1980s), while a metastasizing government crushed the life out of the economy (like the 1930s and what’s happened in the last ten years).”

            no.. what’s been provided is revised history.

            I’m asking for CURRENT REAL WORLD examples not something in the past that is viewed by different people through different ideological lens.

            give me some actual real examples.

            if there used to be actual examples, what happened?

            if they were better, how come they did not survive and prosper better than what they were competing against?

            what I’m hearing – is that – no where on earth, not in 200 countries – is there an example of what you are talking about – and it only used to exist – but did not out compete the other systems and prevail as winners over inferior systems.

            come on Ken.. at some point -you gotta come off the false narrative here..

            what you have right now is a “belief” with no real world examples.. and none that survived that were supposed to be better.

          • I’m not saying the use of technology. I’m saying understanding it

            You have no idea what methods the other OECD countries are using to teach math, but act like you do. I asked you a straight forward example and you gave some half assed example. You have no idea if the other OECD countries are using the tried and true drilling and memorization exercises, without technology that were so effective here in the US, but are now trying to pass off as if you know they are not.

            If you give a middle school class a project to build a robot – they have to be ABLE to read and understand the technologies needed to build it.

            This is the same tragic nonsense that caused an entire generation to have high levels of illiteracy. This type of thinking is what prompted so many in the education field to embrace “whole language” and kick phonics to the curb. The results were utter failure. How do you expect kids to read those instructions if no one taught them how to read? How do expect kids to understand the blue prints for the robot if they don’t understand the math presented in the blueprint? This sink or swim attitude has resulted in an incredibly high sink rate.

            the word problems are the beginning of the rigor

            This is so false as to be absurd. Word problems are the end of rigor. It’s the pretense of rigor and of teaching “real world” problems.

            why not other science? like cancer or tsunamis or asteroid orbits?

            What did I say that made you think I didn’t think these areas of science weren’t politicized? I didn’t mention a lot of areas. Your logic is truly flawed.

            but you’re ignoring the hurricane modelling question here.

            Not really. You’re comparing the model of a hurricane in action for predictions about climate. These are apple and oranges comparisons. You’ll also see that the variances for hurricane evolution in those same models increases to the point of uselessness very quickly, in just a couple days.

            Now compare models for predicting when and where hurricanes will occur with models for predicting climate. They are nonsense models, with no basis in reality.

            it’s not perfect and can be corrupted – no question – but it’s a HELL of a lot better of arm chair science “beliefs”.

            Is it? Giving the pseudo-science of the food pyramid, AGW, and the vaccination/autism and credibility is far more damaging than having arm chair science beliefs about them. Obesity has ballooned in this country due to the horrible food pyramid. Kids have died from diseases that were pretty much eradicated because parents refused vaccination for their children. Literally trillions of dollars world wide have been diverted into bunk “green” technologies for fear of bogus AGW claims. These are all grave damages due to the veneer of credibility of so-called “peer review”.

            I’m asking for CURRENT REAL WORLD examples

            The United States is a “current real world example” of a country in dire financial straights due to an incredibly large and intrusive government.

          • I’m not saying the use of technology. I’m saying understanding it

            You have no idea what methods the other OECD countries are using to teach math, but act like you do.

            How do you know that? but that’s not what I’m claiming anyhow.. what I’m saying is what the testing organizations are saying… both international and American – PISA and NAEP. do you know who NAEP is?

            ” I asked you a straight forward example and you gave some half assed example. You have no idea if the other OECD countries are using the tried and true drilling and memorization exercises, without technology that were so effective here in the US, but are now trying to pass off as if you know they are not.”

            No I do not know how they do drilling but I know of their results and I know what NAEP and PISA say are the differences. DO you want me to show you an example?

            “If you give a middle school class a project to build a robot – they have to be ABLE to read and understand the technologies needed to build it.

            This is the same tragic nonsense that caused an entire generation to have high levels of illiteracy. This type of thinking is what prompted so many in the education field to embrace “whole language” and kick phonics to the curb. The results were utter failure. How do you expect kids to read those instructions if no one taught them how to read? How do expect kids to understand the blue prints for the robot if they don’t understand the math presented in the blueprint? This sink or swim attitude has resulted in an incredibly high sink rate.”

            actually you’re wrong. The whole language and new math and open classrooms were not based on results – on the method.

            Are you actually listening to what I am saying? I’ve said repeatedly that it’s reading, math, and science fundamentals that are at issue. Reading and Math proficiency are what we rank lower on in PISA and NAEP.

            The exact POINT of the robot is that they HAVE TO HAVE all the basics to be able to read and understand what it takes to build a robot. Everything I have said is totally consistent with that including those “word” problems.

            the word problems are the beginning of the rigor

            This is so false as to be absurd. Word problems are the end of rigor. It’s the pretense of rigor and of teaching “real world” problems.

            word problems are simple examples of much more complex real world math.. much more complex than found in the backs of math books.

            you say you teach? you know this guy.. you SHOULD know this. the word problems in the back of textbooks are SIMPLE compared to what you’d have to put in a model for much more complex things.

            What did I say that made you think I didn’t think these areas of science weren’t politicized? I didn’t mention a lot of areas. Your logic is truly flawed.

            nope.. you went for the usual – the climate and I asked about the others and you did not answer.. evaded.

            but you’re ignoring the hurricane modelling question here.

            Not really. You’re comparing the model of a hurricane in action for predictions about climate. These are apple and oranges comparisons. You’ll also see that the variances for hurricane evolution in those same models increases to the point of uselessness very quickly, in just a couple days.

            that’s the point guy. it’s complex and far from perfect and yet you say that climate is “politicized” and I’m asking why hurricane modeling is not.

            “Now compare models for predicting when and where hurricanes will occur with models for predicting climate. They are nonsense models, with no basis in reality.”

            then why do we use them?

            it’s not perfect and can be corrupted – no question – but it’s a HELL of a lot better of arm chair science “beliefs”.

            “Is it? Giving the pseudo-science of the food pyramid, AGW, and the vaccination/autism and credibility is far more damaging than having arm chair science beliefs about them.”

            People who do not have degrees in science nor a decades long career in science – sitting in a chair and reading an internet sound bite are not valid critics.

            “Obesity has ballooned in this country due to the horrible food pyramid. Kids have died from diseases that were pretty much eradicated because parents refused vaccination for their children. Literally trillions of dollars world wide have been diverted into bunk “green” technologies for fear of bogus AGW claims. These are all grave damages due to the veneer of credibility of so-called “peer review”.”

            all of it it? how about SOME of it? and SOME of it has made major progress in understanding.

            you’re putting a “perfect” standard on something that has no perfection. never did. never will. It’s always been 2 steps forward, 1 step back. that’s the way science has always worked – from the time of Newton.

            I’m asking for CURRENT REAL WORLD examples

            The United States is a “current real world example” of a country in dire financial straights due to an incredibly large and intrusive government.

            in your view it is .. but you once again have evaded the question of showing an real world current example of a country that does not do what the US does and as a result has a better economy.

            you have no real examples guy.

            you’re critical of the US but you cannot point to any other country that does things “better” but not doing the things you say are wrong.

            so you’re advocating something for which there are no real examples of.. a theory basically… something that ‘could be’.

            that’s not real guy.

            if you say we have too much regulation and you cannot find a country with less regulation that is “better” then what exactly are you saying?

            yes, we can do better … but doing better with LESS govt and there are no current better examples?

            geesh..

          • How do you know that?

            Because I asked you for an example and you simply said they understand, as if that was some sort of example of a pedogogic method.

            actually you’re wrong

            Actually, I’m not.

            The whole language and new math and open classrooms were not based on results

            You’re claiming that simply giving children blueprints to build a robot will teach them math is based on results? Because if so I’m calling bullshit.

            I’ve said repeatedly that it’s reading, math, and science fundamentals that are at issue.

            The issue is how to teach them. You’re saying the way to teach them is by “real world examples”, like the sink or swim robot method you gave or the failed word problems, both of which fail at much higher rates than drilling and memorization exercises.

            The exact POINT of the robot is that they HAVE TO HAVE all the basics to be able to read and understand what it takes to build a robot.

            Yes. That is the point. You are claiming that these basics will be learned and understood in the course of building the robot. I’m claiming that reading and math need to be understood before attempting to build the robot.

            the word problems in the back of textbooks are SIMPLE compared to what you’d have to put in a model for much more complex things.

            So? Bureaucrats in the government run monopoly are the ones who decide just how complex those problems are. They make it easy on themselves because they get paid the same, regardless of success or failure. The failure on your part is to think these bureaucrats would come up with anything other than these failed word problems in an attempt to introduce “real world problems”.

            the climate and I asked about the others and you did not answer

            Because it’s irrelevant which others. That some are corrupted and politicized is enough to cast doubt on all.

            that’s the point guy.

            So you agree that the models for climate are bunk. Glad to hear it.

            I’m asking why hurricane modeling is not

            There are two reasons. 1) There’s lots of money to be made through government cronyism using fear tactics associated with climate models (ask Al Gore). 2) There are actual consequences to being wrong with predicting hurricanes, which is why weather men are very circumspect about their predictions.

            then why do we use them?

            See Al Gore reference above. The pretense of knowledge gets politicians all tingly and they are more than happy to open up tax payer wallets based on those tingles.

            all of it it?

            Yes.

            an real world current example of a country that does not do what the US does and as a result has a better economy.

            Sweden’s economy was dying in the mid-century and executed many free market reforms and it came out much better for it. The UK under Thatcher. Italy and Greece are crushing themselves out of existence by systematically eliminating free markets.

          • How do you know that?

            Because I asked you for an example and you simply said they understand, as if that was some sort of example of a pedogogic method.

            I did? I don’t think I did guy but I can.. if you want…

            actually you’re wrong

            Actually, I’m not.

            The whole language and new math and open classrooms were not based on results

            and I AGREED!

            You’re claiming that simply giving children blueprints to build a robot will teach them math is based on results? Because if so I’m calling bullshit.

            I’m saying they have to have a rigorous understanding of reading and math – and basic technologies to be able to do that but more than that – I’m saying THAT KIND of project is the KIND of real-world rigor that they need to learn.

            I’ve said repeatedly that it’s reading, math, and science fundamentals that are at issue.

            The issue is how to teach them. You’re saying the way to teach them is by “real world examples”, like the sink or swim robot method you gave or the failed word problems, both of which fail at much higher rates than drilling and memorization exercises.

            no. I’m saying they cannot complete real world analyses if they are not equipped with high skill sets in reading and math.

            in terms of the “right” methods – I do not have an opinion, there are LOTs of different opinions but what I am saying is that none of them are any good if you don’t measure results… performance. You’ll never know what works or not unless you measure results.

            The exact POINT of the robot is that they HAVE TO HAVE all the basics to be able to read and understand what it takes to build a robot.

            Yes. That is the point. You are claiming that these basics will be learned and understood in the course of building the robot. I’m claiming that reading and math need to be understood before attempting to build the robot.

            we’re talking past each other. They need the basics FIRST but once they have them – they need to actually USE those skills in solving a real world problem.

            the word problems in the back of textbooks are SIMPLE compared to what you’d have to put in a model for much more complex things.

            So? Bureaucrats in the government run monopoly are the ones who decide just how complex those problems are. They make it easy on themselves because they get paid the same, regardless of success or failure. The failure on your part is to think these bureaucrats would come up with anything other than these failed word problems in an attempt to introduce “real world problems”.

            OH BS guy.. that’s a cop out and you know it. There is a world of textbooks and beyond that if you don’t like the textbook go find others… that’s no excuse!

            the climate and I asked about the others and you did not answer

            Because it’s irrelevant which others. That some are corrupted and politicized is enough to cast doubt on all.

            ALL – ALL science? seriously? isn’t that anti-science?

            that’s the point guy.

            So you agree that the models for climate are bunk. Glad to hear it.

            I’m asking why hurricane modeling is not

            There are two reasons. 1) There’s lots of money to be made through government cronyism using fear tactics associated with climate models (ask Al Gore). 2) There are actual consequences to being wrong with predicting hurricanes, which is why weather men are very circumspect about their predictions.

            we already agreed they are not THAT accurate guy. In fact, they’re almost never precisely accurate and cities are evacuated that are never touched and other places whacked that were not evacuated…

            but jeeze guy – don’t you think hurricane modellers could also get govt grants and make money ?

            Al Gore.??? jesus h keeerist guy…

            then why do we use them?

            See Al Gore reference above. The pretense of knowledge gets politicians all tingly and they are more than happy to open up tax payer wallets based on those tingles.

            all of it it?

            Yes.

            Good LORD! it’s a global conspiracy?

            an real world current example of a country that does not do what the US does and as a result has a better economy.

            Sweden’s economy was dying in the mid-century and executed many free market reforms and it came out much better for it. The UK under Thatcher. Italy and Greece are crushing themselves out of existence by systematically eliminating free markets.

            okay.. at least you tried here.. credit given… but jesus Ken… Sweden is a welfare state and England has real govt healthcare with real govt doctors!!!

            and all of these countries have the same “liberty crushing” govt policies .. same church different pews, right?

          • I’m saying they have to have a rigorous understanding of reading and math – and basic technologies to be able to do that but more than that – I’m saying THAT KIND of project is the KIND of real-world rigor that they need to learn.

            Of course, the entire point of this thread is how to teach math and reading, but here you are changing the subject into what to do after children all ready learned these skills. Again, you simply assumed away the problem.

            They need the basics FIRST

            Exactly, so why are you changing the subject to what comes next? The entire point of this thread is the dreadful failure to FIRST teach these basics in the US.

            There is a world of textbooks and beyond that if you don’t like the textbook go find others

            What textbooks to use are mandated by law. You can’t simply use another textbook if you don’t like the current one because of the gov monopoly. You could in a free market system, though.

            ALL – ALL science? seriously? isn’t that anti-science?

            Doubt is NOT “anti-science”. Understanding that scientists are people too and subject to the same corruption as everyone else is NOT “anti-science”.

            don’t you think hurricane modellers could also get govt grants and make money

            Not like you can with AGW models saying were going to hell in a hand-basket. Also, hurricane modellers, would like lose their funding if they were as consistently wrong as the IPCC.

            it’s a global conspiracy?

            In the same way gravity is a global conspiracy. If you consistently hear about scientists being politicized, twisting stats to conform to the politically correct narrative, it’s practical to doubt all scientists.

            Sweden is a welfare state

            Not as big a one as it used to be when it was killing itself. And making yourself just well enough not to kill yourself isn’t exactly a shining example of success of the welfare state, particularly with the massive subsidization all of Europe, including Sweden, receives from the US.

            and England has real govt healthcare with real govt doctors

            Backsliding often occurs. And some peoples are just determined to destroy their country.

            same church different pews

            I couldn’t put it better myself.

          • I’m saying they have to have a rigorous understanding of reading and math – and basic technologies to be able to do that but more than that – I’m saying THAT KIND of project is the KIND of real-world rigor that they need to learn.

            Of course, the entire point of this thread is how to teach math and reading, but here you are changing the subject into what to do after children all ready learned these skills. Again, you simply assumed away the problem.

            nope. the point of the thread is the current status of US students which is not good and comments about why.

            They need the basics FIRST

            Exactly, so why are you changing the subject to what comes next? The entire point of this thread is the dreadful failure to FIRST teach these basics in the US.

            remember this: ”

            Scary: Only 57% of college freshman could solve the simple division problem above (231 / 7 = 33) without a calculator (using old-fashioned long division) based on a math assessment test given by Professor Cliff Mass in his Atmospheric Sciences 101 class at the University of Washington.”

            this is way, way past basics

            “There is a world of textbooks and beyond that if you don’t like the textbook go find others

            What textbooks to use are mandated by law. You can’t simply use another textbook if you don’t like the current one because of the gov monopoly. You could in a free market system, though.”

            most schools at the elementary level where basics are taught have defined curricula – that can be taught in a number of different ways -as long as the material is covered and the students demonstrate they’ve learned the material.

            Many states work off of standards. Va uses SOLs and NAEP as well as PALS and Iowa Testing.

            ALL – ALL science? seriously? isn’t that anti-science?

            Doubt is NOT “anti-science”. Understanding that scientists are people too and subject to the same corruption as everyone else is NOT “anti-science”.

            “doubt” of most science on a worldwide basis? geeze..

            don’t you think hurricane modellers could also get govt grants and make money

            Not like you can with AGW models saying were going to hell in a hand-basket. Also, hurricane modellers, would like lose their funding if they were as consistently wrong as the IPCC.

            but the hurricane guys ARE WRONG – ALL THE TIME.

            take a LOOK: http://icons.wxug.com/hurricane/2013/sandy-historical-tracks.jpg

            look at how many models are and how many got it wrong!

            it’s a global conspiracy?

            In the same way gravity is a global conspiracy. If you consistently hear about scientists being politicized, twisting stats to conform to the politically correct narrative, it’s practical to doubt all scientists.

            I guess it depends who you are listening too – all the time but science has never been perfect, has bad actors, has gotten things wrong, it’s just not infallible but the things we have learned and advanced – everything from curing polio to GPS satellites to DNA has also come from “flawed” science …

            half cup?

            Sweden is a welfare state

            Not as big a one as it used to be when it was killing itself. And making yourself just well enough not to kill yourself isn’t exactly a shining example of success of the welfare state, particularly with the massive subsidization all of Europe, including Sweden, receives from the US.

            what subsidies?

            and England has real govt healthcare with real govt doctors

            Backsliding often occurs. And some peoples are just determined to destroy their country.

            been that way since when WWI?

            same church different pews

            I couldn’t put it better myself.

            :-)

  5. Sad part about 231/7 is that is trivial to do in your head. heavens the waste if I had to even find a pad and paper to figure that one let alone boot up.Windows.

    • I didn’t see much of the video. However, you can do 231 / 7 in your head, i.e. (estimating) 7 X 30 = 210 with 21 left over divided by 3 = 3. So, 30 + 3 = 33.

          • I did it in my head much faster (and perfectly) than typing it. There were too may 3s, including Jon’s 3s.

            Also, I may add, I used my fingers, i.e. 210, 20, 30 – two fingers :)

          • According to you, everything happens fast and perfectly in your head. Trouble is, the actual output is usually garbage. Where’s the kink in the process?

      • here’s a video that illustrates what students will need to
        learn if they want to get a job – say working with autonomous vehicles:

        http://www.youtube.com/watch?v=Fo-Y6kEMURk

        this is what kids in the OECD countries are on an academic path to learn and kids in this country, and their parents, and the schools avoid like the plague.

        but it is the 21st century – the technologies that will provide the jobs for those who are educated to 21st century standards.

        “going back to basics” won’t mean much if it is not followed by a lot more academic rigor involving critical thinking associated with real-world problem solving exercises.

      • Well, actually, I went directly to 7 X 30 = 210. However, you can go 7 X 10 and then 70 X 3 and then 10 X 3 = 30 with 21 left over divided by 7 = 3. So, 30 + 3 = 33.

      • Yeah except it is just so much easier to do that one rote.

        231

        lets see 7 goes into 23 3 times, I have two left over and remember that 2 and 1 is 21 which is divisible evenly by seven 3 times

        That is exactly how you do it on paper with the ancient method, and if you can’t remember a “2″ in the process – oh well.

        yeah there are some tricks to multiplication. I don’t know all but a few.

        For instance you can use the quadratic equation to your advantage. Here is one example using (x-n)(x+n) = (x**2 – n**2)

        31 * 29 – yeah, you could probably spend effort and do it in your head. but if you recognize that you have (30 – 1) (30 +1) you got 900 – 1 or 899 – you would conveniently remember the middle terms drop out in an equation like this (x – 1) (x +1) = (x**2 -1)

        So now try it with this

        What is

        18 * 22?

        I read this book “Cheaper by the Dozen” where in one chapter Frank tells how his Father taught them how to multiply huge numbers in the head. Unfortunately he didn’t describe it in enough detail for me to learn it :-( Good book by the way, if you want to read about the Motion study experts Mrs, and Mr Gilbreth and their kin. Very funny book, easy read, lessons about early motion studies. What can you dislike – oh and they are nothing like the recent movies.

        • I think most digit numbers can be done in the head easily because you just use FOIL to do it and you remember the stacks in your head.

          But as you practice you realize things. OK you figured 18 * 22 is 396 right 17 * 23 you subtract 9 from 400 then 16 …

          But what if you have 19 * 22 and you are too lazy to FOIL it in your head? Well 19 = 18 + 1 so 18 * 22 is 396 but you know it is 22 short! so you add that in your head 418. It takes a bit of practice -

          Oh and before anyone complains. I know this is an aside and has nothing to do with the video above.

          • As long as we are at it, to square a number (though there are other techniques) you basically FOIL it but multiply the first and second number and double to get the result.

            42 * 42 is 1600 and 4 – easy enough to add in your head 1604 – but now to get the middle term you multiply 2 * 40 and double it. so 1604 is 160 short, so add that in your head and you get the 1764. Maybe adding 160 to a number is too difficult for some folks. I don’t know. And then you can move about a bit. 42 * 41 you figure 42 * 42 and subtract a 42 like I did in the example above.

  6. Why is that scary? Who cares? When are you going to do anything by hand in the workplace?

    Never.

    I’d say, good job on creating such great calculators that allow us to be many many times more efficient, without having to remember elementary stuff.

    • Actually this solved a problem that even 40 years ago folks who worked at fast food places could not even add. Way back then recall that there was an order pad, and they listed the items and their prices, and then added them up. I liked to compare their version of the total to my version of the total, and called them on overcharges and undercharges more that .10 to .20. Then in 1981 I went to germany and saw the waiters there do the addition in their head and they were right all the time. (So if there is a problem with schools it predates the calculator revolution, as in the early 1970s was when calculators cost over $100.

    • Wow, AIG and I completely agree. :) The whole problem with “education” is that they are teaching such worthless crap, not how they’re teaching it. I haven’t used pen and paper in a decade, let alone scratching out subtraction by hand. Of course, I’m an engineer, so I can do such trivial calculations in my head. If it’s larger numbers, say 2,234,324 divided by 1875, I first estimate it- comes out to a bit more than a thousand- then type it into my computer if I need a more precise answer, ie 1191.64.

      Understanding what addition or subtraction represent and perhaps some basic estimation of orders of magnitude, which most journalists do not even seem to grasp, is all that most people should be taught. Wasting time on various implementations and algorithms is just make-work for the kids and teachers’ unions, who wouldn’t know what is useful if their life depended on it. This is why online learning is going to decimate the schools and universities, because the existing curriculum is completely worthless, not because online is so much more efficient, though it is that too. As long as online learning consists of simply slapping the old curricula online, as dumb efforts like Khan Academy do, they are almost as worthless as the schools they’re trying to replace.

      • It is interesting that even common folk 1000 years ago probably had 100x the capacity for memorizing. The reason without writing, and reading that was the only way to keep vital information. Apparently it was too the point where the travelling bard could come and give a speach in song for an hour, and everyone in the audience would have it memorized after listening once.

        The invention of the cheap book, caused us to have a decline – and with large populations writing and cheaper linen paper you don’t have to memorize every event when you can now read, and the information is easily referenced in a book. And nowadays in the Interwebs. And actually the last nail was the invention of Indexing!

        One of the videos in the “The Day the Universe Changed” by James Burke is a fun look at how this change happened. I will post a link to it if I can find it tonight.

        • Here is the episode of Day the Universe Changed.

          http://www.youtube.com/watch?v=9D3elWaqgbo
          Unfortunately I think it is slightly more slow paced than some of the others, but it discusses how we lost our memory. If you get into is and want to see the others I would recommend skipping episode one. And for Connections episode 10 and possibly 1. They are just introductory and conclusion episodes – not much meat.

    • Why is that scary? Who cares? When are you going to do anything by hand in the workplace?

      That’s right. Nothing bad has ever happened by simply trusting others that their math is correct. No one ever bought a mortgage or invested their money had anything bad, financially, happen to them by simply trusting other people’s math, right?

      • What does using a calculator or financial software to do your calculations have to do “with trusting other people’s math?” Either way, you can check the math, but the software will do it hundreds of times faster. :)

        • It is nice to be able to string three numbers together, without pulling up a spreadsheet every time. Use technology as a tool, not a crutch.

          • re: ” It is nice to be able to string three numbers together, without pulling up a spreadsheet every time. Use technology as a tool, not a crutch.”

            totally agree.

            working in software – how does someone who codes an equation like these:

            http://en.wikipedia.org/wiki/Orbital_mechanics

            how do they know they’ve coded them correctly?

            it’s tricky programming equations in different programming languages and not easy to validate them especially when there are many lines of code – each line dependent on the math resulted generated from the code on the line above it.

            here’s orbital period for example:

            T = 2pi * square root (a cubed / u)

            where a = length of semi-major axis
            and u = is standard gravitational parameter,

            and this is one equation, one of dozens, hundreds in a orbital model for a vehicle in which you are seeking to find a point where the object will land – or will be at some point in time.

            these are things you don’t do in your head, and you don’t do (much) of it even on a calculator.. but you encode it in a programming language to run on a computer but then you have to validate that what you encoded was exactly the correct programming representation of the equation.

            even after that – you get into issues of how many digits of accuracy the computer has and whether you have to go to double precision or not ….etc…etc

            this is what you need or orbital mechanics.

            there is a similar discipline for other kinds of vehicles in other kids of 3-dimensional environments like sea or land.

            You cannot begin to do this kind of work without a heavy duty foundation in math and science and language (to read and understand) – that starts in K-12 and continues into college with BS/MS degrees in various associated hard science disciplines.

            You can’t do this stuff by viewing a Kahn Academy video. You might if you viewed dozens or hundreds of them.. progressing from basic differential equations and going forward to orbital mechanics or similar.

            these are representative of some of the jobs in the 21st century that our kids will compete for.

    • “Wow, AIG and I completely agree”

      Ok. I’ve changed my mind! :) Down with calculators!!!!!

      I haven’t done math by hand in many many years. 99% of the calculations I have had to do, both as an engineer and now as a PhD student are not one-off little calculations where bringing up a calculator takes longer than doing it by hand.

      99% of calculations people do in the real world, are whole sets of calculations. You’re doing calculations over a set of numbers.

      Under those situations, i.e. most of what we do in the real world…Excel works miracles.

      But even if we think 1-off calculations, every phone or computer has a calculator. So 99.9% of people are no further away than their pocket from a calculator.

      Our inability to do simple math is precisely what allows us to do hard stuff better.

  7. The sad part is, it would probably be best to teach all these ways to kids with the traditional algorithm taught as the tool to power through when things get tough.

    To “study” you need different views to compare and contrast. It is from such thought that you learn.

    The really sad part is even the hint of going to the calculator. Sure, there are calculators but the kid needs to learn how to do it the hard way to understand what is going on. So the calculator or computer isn’t a magic box but is a tool that does mundane tasks after you’ve mastered the task by hand.

    Our modern methods actually mean that the student is doing things the “inefficient” way. Why? Because the student isn’t doing production, they are developing new ways of thinking, or ordering the world. When they’ve got that, they can turn the mundane over to the magic boxes.

    School has become to enamored with the easily measured fact accumulation and is increasingly missing that those facts are just the means of demonstrating and inducing the more disciplined ways of thinking. Memorization of the times tables should lead to the student seeing the relationship between numbers and the basic rules. Long lost is the pen/ink drafting that teaches the student how to think 3 dimensionally in ways CAD programs never can. Hand tools teach the nature of the materials in ways covered up by the use of power tools.

    But instead of trying to get a student to think about the Renaissance they are pushed to be able to reproduce 8 reasons for it without thought on tests or recitation.

  8. So I actually sat down and watched that video: I disagree with her on practically every point. To begin with, when she started showing the “traditional” methods, I realized that I had forgotten the traditional methods. I had some vague recollection how you begin, but couldn’t remember the steps. Is this because I’m some writer or other “artsy fartsy” type who never deals with math? No, I’m an engineer, who can do more math in my head and faster than most can type it into a calculator.

    Like most kids, I learned the traditional methods in elementary school decades ago and then never used them again, even in my highly mathematical engineering education. When I was studying engineering in college, I’d either do the math in my head or punch it into my scientific calculator: writing it out by hand never crossed my mind. In fact, the TERC method is basically what I do whenever I do math in my head, guesstimating the answer and then refining as I go. I see the value in the other alternative methods also, as they teach better what multiplication and division mean as opposed to how to execute it, because the kids will frankly never need to execute it. The only exception might be that lattice method, which seems as arcane as the traditional method.

    In fact the best route to multiply 26 times 31 is just to estimate it, ie it’s about 25 times 30 and I know 3 times 25 is 75, so I know it’s a bit more than 750. Or round to 30 times 30, you know that’s 900 if you know 3 times 3 is 9 and 10 times 10 is 100. Either answer is off by around 10% from the real answer of 806, but for most purposes, you’re not going to care. If you really did, punch it into a calculator.

    Drilling kids in these methods more, as she calls for, is stupid in the extreme, as they will never use them again. She might as well call for them all to learn how to knit, that’s how dumb it is, and I’m sure that’s what she would have called for a century ago. When I was in high school and they had such drills in algebra class for homework, I got bored and just stopped doing it. I knew how to do it, so why do it over and over again? As it was part of my grade to do the homework drills, I didn’t get a great grade in that class. Did it hurt my education? Nope, I took a ton of engineering and some graduate math in college, and math were always my easiest classes, automatic As. :)

    Online learning revolutionizes education much more than it does the news or media. We just don’t know it yet, because it takes a little more effort than to simply slap the news online. This is why every current school and university will be dead and gone in a decade or two, just as all the newspapers are dying out today. Good riddance. :D

    • Sorry, that should be “graphing calculator,” not “scientific calculator,” that I used in college. I haven’t used either in so long that I had forgotten the right terminology and had to just look it up on Wikipedia! No joke.

      You can buy a $100 smartphone these days and find an app that does more than my graphing calculator did back then, is a hundred times as powerful at number-crunching, and won’t take seconds to display a graph like that old HP used to. :) Soon, the same smartphone will be less than $25- hell, you could probably build an adequate smartphone at that price now, they just don’t because nobody wants to buy something so “underpowered” by today’s standards- just as you can now buy cell phones, ie the old dumb phones, for less than $10.

      • It is amazing – people don’t realize the supercomputer power they have in their pockets. If reprogrammed to do say “Bank of America’s” billing the way was done in the 1970′s you have the power in your pocket to handle the entire database, data input and output, and sending out the processed statements. We end up using all that power mostly for neeto graphics and fun image viewing today, rather than hard core industrial and financial uses. (Note for those who don’t believe this – we send data on our phones via 4G and wireless now about 10x – 20x faster than the mainframe “channel” could)

        And we take for granted that there is just an app for that. I have found apps to tune a violin, metronome, to measure your heartbeat, compass, flashlight, instant teller (well I can’t get cash – yet) in addition to standard apps, like radio, movie player, book reader … And just 10 years ago these would all be 20 separate devices costing you hundreds of dollars or require I have to stand in line for an hour at the bank. And I paid just $350 for my no contract phone.

        • I actually did some research today. Cray 2 computer with 4 processors , and which needed to be cooled in freon which bubbled due to the heat, could do

          1.9 billion 64 bit floating point operations per second. It was introduced in 1985 and was the fastest computer in the world. My middling phone with an Qualcomm Snapdragon S4 pro (2 years old now) with 4 processors can do 1.2 billion 64 bit floats with IEEE 80 bit precision. Or using the NEON instruction set, which only does 64 bit and not to IEEE precision, which is probably more like the Cray – 4 billion – or twice as fast. And while it gets a bit warm, it doesn’t need a cryogenic cooling system.

          Scientists were happy to get a small slice of time on the Cray for research- today we use that power to play Angry Birds – that is just amazing.

    • I actually like to write stuff out. I use calculators, but if it is just a few numbers why waste the effort. Part of the reason is that most of my engineering companies I work for are too cheap to get me a calculator, indicating that I should use the one built into Windows – which is really slow going. Much quicker to just write the 2 – 3 numbers down and do it on paper.

    • “In fact the best route to multiply 26 times 31 is just to estimate it,”

      I would do it quickly and mentally this way with an exact result: 3 times 26 is 78 times 10 is 780 + 26 is 806 and then check it with a calculator or spreadsheet if it is important. To each his own.

      • I know elementary teachers that teach kids math in other base systems – like base 8 or base 4 – as a way to get them to think about what they are doing and why.

        • I can see why the first-trade math teaching angle could be a useful tool for some students. If a student has 3 one hundred dollar bills, five ten dollar bills, and two ones, that is not the same thing as having 352 one dollar bills. Most of us at our level who follow Carpe Diem cannot see the difference because we very easily mentally process through the difference.

          • ” Most of us at our level who follow Carpe Diem cannot see the difference because we very easily mentally process through the difference.”

            so they can do math in Base 3 or 7 or Base 2 ( a favorite for computers)?

            and you can convert from base 7 to base 10 for say 253?

            the word I get is that some kids get this quick and others it’s a struggle.

    • “In fact the best route to multiply 26 times 31 is just to estimate it,”

      I would do it quickly and mentally this way with an exact result: 3 times 26 is 78 times 10 is 780 + 26 is 806 and then check it with a calculator or spreadsheet if it is important. To each his own.

      • You can see I learned math on a slide rule because powers of plus or minus 10 are automatic to me. I also mentally process changing subtraction to division and addition to multiplication. I don’t think I would teach math using a slide rule, but I think my math skills are stronger because I learned that way (or maybe because I am a white male).

  9. What’s striking here is how many people who have been exposed to the new methods are willing – and able – to defend them.

    I would have poo-poohed the new methods too, but I know adults who say they learned more about math while helping children through these methods, than they ever learned at school. So I don’t poo-pooh these methods any more.

    • re: “the methods”

      If we made our goal – academic performance – as do the OECD countries, it would not matter as much.

      The easier way would be to model what OECD does since it has proven to work.

      but if we wanted to do it different (not sure why), then at the least – we should, with every method – measure.

      we should want to know if the method chosen is effective or not and not just assert that it is because “research” or pick your reason – but the only thing that really matters – is – is it effective?

      No matter what kind of schools we have (or not) if we embraced proof of performance as a required metric – we would advance.

      we know right now that the two key areas where we are deficit is: 1. being able to understand and articulated real world problem solving with math, reading and science

      and… critical thinking in using these tools…

      we do not teach either in many American schools whereas these things are mandatory is virtually all OECD schools.

      When we implement these requirements in our schools like New York and Virginia recently have – the result is
      that standardized test scores – PLUMMET – precisely because the tests are showing that we are not teaching the academic rigor that is necessary for young people to effectively compete for 21st century jobs.

      Instead of confronting the realities here – we seem to be having arguments about things like “bad teachers”, “bad schools”, unions, private/charter schools and instead of making OECD standards the goal – we actually oppose testing … and want to “revert” to 1950 type math.

      How can all he OECD countries get this right and the US get things so screwed up?

      • “Instead of confronting the realities here – we seem to be having arguments about things like “bad teachers”, “bad schools”, unions, private/charter schools..”

        As always, Lartard wants to keep the focus away from any kind of accountability for the people who are in charge of actually, you know, educating people.

        • ” “Instead of confronting the realities here – we seem to be having arguments about things like “bad teachers”, “bad schools”, unions, private/charter schools..”

          As always, Lartard wants to keep the focus away from any kind of accountability for the people who are in charge of actually, you know, educating people.”

          actually I’m FOR – ACCOUNTABILITY – not only for public schools but the non-public ones that are claimed to be superior.

          So far, the folks who want non-public schools seem not too keen on accountability… rather than wanting it.

          and for the non-public schools that DO HAVE some level of accountability – the results are MIXED- ESPECIALLY for the harder-to-teach demographics.

          • “actually I’m FOR – ACCOUNTABILITY – not only for public schools but the non-public ones that are claimed to be superior.”

            Oh, give it a rest. All you do is spout the union talking points your wife brings home.

  10. Who else got a headache from that video? my friend’s brilliant teenaged daughter complains about this free-form crap math all the time. It’s meant to engage the dumb kids, but I can’t see how it would do anything other than confuse them.

    I did briefly teach algebra to high school students and I do appreciate the value of finding ways to make math understandable to kids who don’t get it instantly like “think of geometry as building. To build a house, you must first have a foundation, only then can you put up walls and only when you have walls you can build a roof. Similarly, to build a triangle…..”. I worked with a couple of students with learning disabilities who responded well to thinking of solving for the variable as “excavating” the variable or “digging” for the variable. these are ways to make basic math (which really can’t even be called “math”) approachable. “Reform” math, however, adds complications so that NOBODY can understand it.

    • I have to say I have learned more from the math books as well from my young kids. You have to figure out what the heck they are trying to teach in the book, so you can decypher and teach the kids the more traditional way and explain what it was really about.

      I was a math tutor in College, and I have to say the worst people to help were the education students.

      Their books were all new math, and the goal was to figure out how the student did things so you could mark them correctly for creativity in addition to giving a score for correctness. Dang some of the creative examples were pretty interesting – and I could figure them out – then having to explain what the “student” did to the prospective teacher, was actually the tough part. These weren’t algebra, just crazy ways to Add, Subtract and Multiply and Divide standard numbers. In the end I was left wondering, why were they letting these kids fend for themselves. Creativity is all good, but if you have come up with an effective tool or two, why force the kids to reinvent everything ineffectively by themselves. I think think this was the mid 90′s new teach, which has been abandoned for what is above.

      • re: high school/college “new” math.

        My experience is when you enroll in a course called Differential Equations – the math is not “new” but pretty old and established.

        and if you want to work in a field where computer models are used for thinks like moving vehicles – whether they are on land, under-sea, in the sky or in orbit – you must understand differential equations and spherical trig and Linear Matrices, etc…

        and that level of knowledge is way over the concept of whether someone knows how to do long-division or have a “feel” for numbers.

        here are examples of the equations you need to understand, know how to manipulate and code into a software model if you are going to be successful:

        http://en.wikipedia.org/wiki/Orbital_mechanics

        note also – that these are not “beliefs” of people about certain theories. there is a reason why this is called “hard” science and basic theories are the starting point for modelling real world circumstances – not the end point.

      • Marque2,

        As a kid, I took some non-traditional approaches to learning math myself. I always wanted to know WHY things worked the way they did and I was terrible at rote memorization of equations. So, I ended up actually re-inventing the wheel a few times. I once told one of my teachers that I had no head for math and she replied that I was in a pretty advanced math class for someone who can’t do math and asked to see how I actually approached problems. I showed her and she told me that’s exactly what mathematicians did to create formulas. Once I got the logic, the formula was obvious and I remembered it fine. It’s a huge time sucker to go through this rigmarole every time.

        However, the idea of assigning points for creativity is ridiculous. The kind of “math” we do in school is all about arriving at the correct answer. If you have to stand on your head and visualize walnuts to get there, fine, but that shouldn’t be rewarded because there’s nothing particularly special about simply adjusting inputs to your own brain’s natural function. We all do that.

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