A Constructivist Math Example

Yesterday someone reminded me about this great video which I shared with people a long time ago.  If you weren’t involved back then, you may not have seen it and wonder what constructivist math is like.  M.J. McDermott is a meteorologist in Washington state who was involved in trying to improve math education and made this video a few years back to show how Investigations math style teaching works. Prepare to be dumbfounded. Is it any wonder kids are falling farther and farther behind?

11 thoughts on “A Constructivist Math Example”

  1. The information presented in the video does not show a huge increase in movement toward the dumbing-down of America’s educational system; however, if you can play the devil’s advocate and work out a method of decreasing the ability of America’s young people to compete globally, or to achieve the very best in learning methodology, you would want to begin so very slowly so as not to make the process transparent. You would want to do something to get your foot in the door, even if you have to begin the process by promoting a change that “appears” for the better.

    The minds behind the curriculum development that will eventually be effective in dumb-down America’s youth are brilliant. They “sell” the idea to “retarded” adults who accept their initial ideas. From then on it becomes easier to move the program along, and over two or three generations, America will be filled with people who fall far behind the populations of third world countries. We can become a nation of educated fools if we allow any concepts, principles, values, or methodologies from sources which we know are hell-bent on destroying the economic and military power of the U.S.

    The small methodologies in learning math, as are so well explained in the video, are nothing more than “foot-in-the-door”, or a “first-step”, in the dumbing-down process. In fact, it is actually a “second-step”, or “third-step” if you take into account the mind-set of those who accept and push for these changes in math methodology. Their minds have already been set up to accept these new methods, and whether they are acting deliberately, or as dupes, their acceptance of changing that which has made America the best in the world, will certainly bring our country down from that level of achievement.

    Here is a reality situation – and let us assume Common Core’s standardized testing has been adopted also:
    1. A K-12 curriculum in math is developed, sold to local administrators/teachers/school boards/parents.
    2. They accept the curriculum and dictate to the teachers that this is what will be taught.
    3. As each of five or six years comes and goes, Common Core’s standardized tests will indicate the students are increasingly falling behind.
    4. More inputs are pumped into the school’s math program (raising the cost of education per pupil).
    5. The school districts become frantic over how badly the students are falling behind in their test scores, but they are now five or six years into the program, and to start all over and go back to the any original math methodologies would be declared “regressive” and will not work.
    6. The USOE has used these five or six years to implement additional “dumbing-down” ideas, the cost of education has gone through the roof, student’s are unable to compete, Common Core’s standardized testing procedures are never a part of the evaluation process to solve the problem, and now the USOE is offering (or possibly, by that time, demanding) to take over control of the local schools in order to solve the problems.
    7. A few citizens will object, but the way the country is going, it is evident they would quickly be silenced.

    Such a “progressive” process is an example of what is in the minds of those who are deliberately trying to socialize America. And without an “America” (as in the traditions of it’s founding fathers), there will be no power to prevent someone with a Stalin-, or Hitler-type mind from moving our country directly to communism or fascism. For people to realize this picture, they will have to see the end from the beginning, understand the mind-set of those who attempt to convince us of the need to adopt these methodologies presented in the video, learn about the different “think-tank pools” of people who come up with and push these ideas, and be able to understand all the intricate aspects that are being laid into place to nudge (little-by-little) America over the cliff. In my mind, and based on my moral foundation, it is evil in design, and currently incredibly well set into place throughout the fabric of our society and within the mind-set of far too many Americans.

  2. The video correctly and repeatedly makes the point that the “new” ways of teaching math assume that students will use a calculator. The basic problem with that assumption is that in order for the students to use a calculator, someone must know how to build the calculator. This is something I would like my children to be able to accomplish, and I assume that many reading this have similar feelings.

    Building the calculator requires understanding how to build the microprocessor that runs the calculator. Building the microcontroller requires understanding chemistry, physics, and manufacturing processes, all of which require a solid understanding of math. Furthermore, it requires planning the input and output user interfaces, as well as the printed circuit board providing connections between all of the components, again requiring good logical skills. Next, it requires understanding how to program the microcontroller. The microcontroller is controlled by Assembly language, and essentially performs all of its functions by either 1) moving a series of binary digits into a register, or 2) adding a series of binary digits to that register. The algorithms used must therefore seamlessly allow flow from decimal to binary and hexadecimal (used to abbreviate 4 binary digits in a single base 16 digit), must then break down to a series of additions, and lastly flow back to decimal.

    The speed at which the calculator performs its work is determined by 1) the clock speed at which the hardware can run (with 1 Assembly code step occurring at each rising clock edge) and 2) the efficiency of the software algorithm (remember that term from the video). Today’s hardware is already functioning so fast that significant gains in speed cannot occur without overheating the silicon from which the microcontroller is formed. Therefore, speed depends on an efficient algorithm.

    Traditional math teaching methods provide efficient algorithms that enable students to gain the high level of math proficiency needed to do all of the above. If we are going to produce students who can build the calculator rather than simply depend on them, we must stick with traditional math.

  3. You can’t necessarily compare the achievement of today’s kids to that of 10 or 20+ years ago and expect all of that to be connected solely to education. Society is not the same as it was before, including the make-up of its population, the relative importance education has in society and the average income vs. hours worked for families. To think that a newer way of teaching is the sole factor is to ignore many variables that exist. Rather than making judgments based on a video, perhaps it would be better to apply a more mathematical approach, and see how students perform using this method in comparable schools to those using the standard method. Better yet, do a longitudinal study to compare how these students perform 5 or 10 years down the line in math classes. None of the reasons that have been given actually are backed up with any evidence of any sort.

    I also don’t think that America is being dumbed-down through education for some evil ulterior reason. Also, completely illogical, especially considering this is a thread about math education, which would actually suggest that the lack of logic being presented in discussions like this might be something to examine as the reason why “America” (according to forefathers) is not what you would like it to be. You would be better off blaming the average consumer and big box stores for pushing for cheaper goods (and bigger profits) and moving manufacturing to places where they can pay employees very little, like China (the rising World power, whether we like it or not). Or a myriad of other reasons. There is rarely just one cause to a problem, and we are all complicit in some way.

  4. To Big Picture, you’re right that there isn’t just one reason the education system is failing. There are many. Constructivism is just one prime example. If you want a detailed, documented look at the big picture behind this, go to http://www.deliberatedumbingdown.com and get the free pdf book that Charlotte Iserbyt wrote which contains tons of documents she gathered while working at the US Dept. of Education. Today, we face Common Core, a corporate takeover of education. On the other side we have the socialists and outright communists like Bill Ayers looking to use the education system to promote their specific political agenda. It’s all out in the open if you look at it with open eyes.

    1. This video doesn’t disprove constructivist math. It doesn’t even cover an example of constructivist math. You only show that some algorithms and approaches to solving multiplication/division are less efficient than others. To be clear, i prefer the old-school style of multiplication and division. But you don’t disprove constructivist teaching as a whole approach to education here. You’re only debunking the use of these approaches. You can engage in constructivist math using the tried & true algorithm.

  5. The video has no place here as the host has no credibility. She has no teaching credentials and no degree in teaching children. Furthermore, all children are not the same. They learn in different ways and styles. If a teacher can use one of the above mentioned methods to make a breakthrough with one student in math, that’s a gain. But to run down an entire curriculum is wrong, ESPECIALLY if you’re not a veteran teacher or have any teaching experience. What’s wrong with public education in THIS country is everyone sticking their nose into it when they don’t have experience or education in teaching.

    1. Jay, to say that because someone doesn’t have credentials in education means they can’t demonstrate how a math problem works in a certain philosophy and then criticize it is silly. I doubt any of the nonsense methods taught in Investigations math make breakthroughs for students. In fact, there are no studies whatsoever that show constructivism as a useful pedagogy (http://www.oaknorton.com/mathupdates/20080903.cfm). Look up Project Follow Through as well. What’s wrong with education in this country is that people at the top think they’re smarter than everyone else and impose dangerous education fads on children. It’s time for true local control of education by terminating the federal DoEd and having states allow schools and districts to decide with parents on how to teach their children.

    2. yes but if a student put down 6 for 36/6 then that should be the end of it. I just retired from medicine and we use algorithms for a lot of therapy and diagnosis. I was in grade school 65 years ago and as I remember we used the traditional methods, but there were plenty of word problems to teach how to use those skills that we had learnt to solve problems.

  6. Math gives children the ability to look for what is missing. Math is necessary for children to employ daily life facts for understanding. We all learn from good and bad outcomes but what if we want an optimal outcome? Without math skills we may be able to function in daily life but a person will be greatly hampered if they want to change their lot in life but do not know how to look for and employ missing information. Math teaches a child how to think in an orderly manner. Math life skills application reaches far beyond algorithms.

  7. Wonderful video! She hit the nail on the head! I, an elementary school teacher, was forced to expose my students to the horrors of Everyday Math. Math fact practice and standard algorithms were practically ignored in this program. Only the 2’s, 5’s, and 10’s multiplication facts were required to be memorized. The underlying rationale was that this information could be used to construct strategies for figuring out the rest of the multiplication facts. Without quick retrieval of multiplication facts, students spent an exorbitant amount of time trying to find the least common denominator in fraction work or finding the value of “a” in a simple pre-algebra example requiring division. Sixth graders were frantically drawing pictures, filling up paper with trial and error attempts, repeatedly adding, counting on their fingers, resorting to making arrays and tallies–just to find the answers to basic problems with a step or 2 that involved multiplication or division. Most assignments were carried out in “collaborative” groups, which really boiled down to 1 or 2 students do all of the work and the rest of the group “blindly” copies.
    This constructivist approach did NOT benefit the majority of our students. Instead, most felt confused, frustrated, or indifferent. We tried Everyday Math for more than 10 years. Help! I would warn all schools to run away from this program.

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