Weekly Math Updates

July 11th , 2008


  • Constructivism Article
  • Media Articles
  • Cool Software

Hi folks,

There's a number of things going on right now that over the next few weeks should come to light and will require a renewed effort on your part to spread the news far and wide. Be excited!

Constructivism Article

I stumbled across this excellent article while doing some research a couple weeks ago.



The purpose of the research was to look for parallels between constructivism and communism.  Both philosophies have at the root of them that there are no absolutes.  The first media article listed in the next section also mentions this about constructivism.  In the case of communism, it was justification for athiesm and banishment of God.  There is no absolute way to tell God exists so the state is the only absolute. The parallels don't end there but I'm going to keep this as short as possible and just share a few quotes from the article and one other site.

What is Constructivism?

From : http://www.funderstanding.com/constructivism.cfm (shortened and emphasis is mine)

Constructivism: a philosophy of learning founded on the premise that, by reflecting on our experiences, we construct our own understanding of the world we live in.
Guiding principles of Constructivism
1) Learning is a search for meaning.
2) Meaning requires understanding wholes as well as parts. The learning process focuses on primary concepts, not isolated facts.
3) In order to teach well, we must understand the mental models that students use to perceive the world and the assumptions they make to support those models.
4) The purpose of learning is for an individual to construct his or her own meaning, not just memorize the "right" answers and regurgitate someone else's meaning. Since education is inherently interdisciplinary, the only valuable way to measure learning is to make the assessment part of the learning process, ensuring it provides students with information on the quality of their learning.

How Constructivism Impacts Learning
Curriculum--Constructivism calls for the elimination of a standardized curriculum. Instead, it promotes using curricula customized to the students' prior knowledge. Also, it emphasizes hands-on problem solving.
Instruction--Under the theory of constructivism, educators focus on making connections between facts and fostering new understanding in students. Instructors tailor their teaching strategies to student responses and encourage students to analyze, interpret, and predict information. Teachers also rely heavily on open-ended questions and promote extensive dialogue among students.
Assessment--Constructivism calls for the elimination of grades and standardized testing. Instead, assessment becomes part of the learning process so that students play a larger role in judging their own progress.

In short, constructivism promotes no measurement of learning and in fact promotes the idea that students should be ever pondering and never arriving at an end.

From the paper I mentioned at the beginning "Constructivism in Science and Mathematics Education" by Michael Matthews (University of New South Wales, Sydney, Australia), come the following quotes:

Grayson Wheatley offered a ... summary of the epistemological core of constructivism, saying:

The theory of constructivism rests on two main principles. . . . Principle one states that knowledge is not passively received, but is actively built up by the cognizing subject. . . . Principle two states that the function of cognition is adaptive and serves the organisation of the experiential world, not the discovery of ontological reality. . . . Thus we do not find truth but construct viable explanations of our experiences.  (Wheatley 1991, p. 10)

Constructivism, in all its varieties, has been the subject of heated debate.  The debate is not simply about the adequacy of a particular learning theory, or the cogency of a epistemological position.  Something more is at stake.  Karl Popper recognised it when he wrote:

... But the belief in the possibility of a rule of law, of justice, and of freedom, can hardly survive the acceptance of an epistemology which teaches that there are no objective facts; not merely in this particular case, but in any other case.  (Popper, 1963, p. 5)

He quotes Michael Devitt as saying:

I have a candidate for the most dangerous contemporary intellectual tendency, it is ... constructivism.  Constructivism is a combination of two Kantian ideas with twentieth-century relativism.  The two Kantian ideas are, first, that we make the known world by imposing concepts, and, second, that the independent world is (at most) a mere 'thing-in-itself' forever beyond our ken. ...[considering] its role in France, in the social sciences, in literature departments, and in some largely well-meaning, but confused, political movements [it] has led to a veritable epidemic of 'worldmaking'.  Constructivism attacks the immune system that saves us from silliness.  (Devitt 1991, p.ix).

Mr. Matthews concludes his paper with this statement:

Given the influence of constructivism on education reform, teacher education, curriculum development and pedagogy, it is important to be clear about just what are, and are not, the epistemological commitments of constructivism.  And what relationship these commitments have, if any, to classroom practice.  The history of education is littered with ‘ideas that seemed good at the time’, but whose enactment caused educational and cultural havoc.  Constructivism has all the earmarks of being such an idea.

How can we hope to stimulate children's minds and transmit the knowledge of the ages to them when we make them start from scratch and make them question that even the things that are true that they learn might not be true?  It's the Sunday School class where they tell students, "We won't be studying the Bible anymore but rather want you to go out and learn for yourself how to deal with pornography.  Nothing is absolute.  Have fun." 

This perversion of morality is being played out in school classes with devastating results.  The math war is far from over as long as such philosophies are not exposed for their falsehoods.


Media Articles

Return of the Math Wars

"1997 saw the height of the Math Wars in California. On the one side stood educrats who advocated mushy math -- or new-new math. They sought to de-emphasize math skills, such as multiplication and solving numeric equations, in favor of pushing students to write about math and how they might solve a problem. Their unofficial motto was: There is no right answer. (Even to 2 plus 2.) They were clever. They knew how to make it seem as if they were pushing for more rigor, as they dumbed down curricula."

Utah State mixed over findings of math study

A recent national study critical of K-6 teachers’ preparation in mathematics has drawn mixed reactions at Utah State University.

Utah State was the only school in the state included in the National Council on Teacher Quality survey and was listed as “failing on all measures” in its efforts to train elementary education majors to teach math.


“There are problems with the study,” he said. “I think one criterion that is missing is what our teachers end up doing in the classroom with their students. When judged on that, if you look at superintendent and principal’s ratings of our graduates, they are quite extraordinary.”

At the same time, Dorward agreed that USU’s elementary education major offers “very minimal preparation” in math instruction.


State to make student test scores accessible online

In a word... FINALLY!!!  This is the digital bridge that Senator Stephenson has been working so hard on to make everyone instantly accountable for performance on tests. 

The state has decided to award $7.5 million to DigitalBridge to create the statewide data system lawmakers called for in 2007. The system will allow teachers and parents to track online their children's test scores, the test scores of their children's classrooms and those of other classrooms and schools, said Patti Harrington, state superintendent. School transcripts also will be kept electronically so they can be transferred more easily between schools when children move.
    "When a child moves, even just down the street, sometimes it will take more than just a few days to get information down to the next campus," Harrington said. "We want that to be immediate."

Utah districts, charter schools will share $20M in merit pay

Don't know much about the details on this.  In Singapore they have a way to measure the value-added by a teacher and I sort of doubt that system is what is being done here. It would be nice to say "here's the starting scores for your class and where you got them to at year end."  It would also be nice to contrast this with "Teacher of the Year" teachers and see how they really stack up where it counts instead of the politics played within hierarchies.

"At least 31 Utah school districts and charter schools will get a piece of $20 million to pay teachers for performance next school year.
    In all, 85 districts and charter schools submitted widely varying plans to the state Board of Education on how to pay employees next year for performance beyond their normal salaries, which are based on experience and education.


From the "How did they graduate?" camp...

Dallas county official: “Black hole” is racist! (MUST READ-SHORT)


From the "it can always be worse" camp...

Boys punished with detention for refusing to pray to Allah

"Two seventh-grade boys were given detention and their classmates forced to miss their scheduled refreshment break when the pair refused to kneel and pray to Allah during a religious studies class.

Outraged parents called the punishment of the boys for not wanting to take part in the practical demonstration at Alsager High School near Stoke-on-Trent, UK, of how Muslims' worship Allah a breach of their human rights."


This is pretty interesting stuff as well.

Mystery tablet could redefine Jewish-Christian links


Cool Software


Scroll down and look at a couple of the videos.  Looks like the software is pretty intuitive, which it has to be since it also appears to have Japanese icons in the program.  Looks very cool though.


Till next time,

Oak Norton

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