Fuzzy math and other nonsense in the classroom ...

[thisnumbersdisconnected]

http://www.foxnews.com/us/2013/08/30/new-age-education-fuzzy-math-and-less-fiction/

If the new national Common Core educational standards influence curriculum the way some fear they will, students can say goodbye to literary classics and hello to fuzzy math, say critics.

The Common Core State Standards initiative, a plan devised by the nation's governors and backed by the Obama administration, seeks to set a uniform standard for grades K-12, to ensure kids all over the nation reach the same minimum level of learning. Some 45 states, in many cases enticed by federal grants, have signed on and testing of students in grades 3-8 and once in high school is scheduled to begin next year.

Supporters say Common Core only tests students in math and English, but critics say school districts will devise curriculum to maximize their students' performance on the national exams, and, in fact, have already begun that measure. And those same critics claim Common Core math standards barely cover basic geometry or second-year algebra and that the classics are all but ignored in English classes​

Health care. Foreign policy. The economy. The war on terror. All botched and turned into disasters by this obscenely inept administration. And now they're turning to education, with the help of the nation's governors.

 

[Scarlett O.]

My students have gone to P.E., so I am responding to this in an empty classroom.

I don't have much time say anything except that this "report" by Fox News (which I typically enjoy) is not credible.

And I keep seeing opinion after opinion, typically from fundamentalist Christians and/or public school haters who "CLAIM" to know all about common core. Yet they opinions betray the fact that they know nothing and are parroting someone else. And that is ignorance.

I would LOVE to actually see one of these "reporters" actually LOOK at the common core curriculum and THEN give an opinion .... an opinion based on research and not the gossipy criticisms of those who despise public schools.

Be rest assured it's hard. And no, just because you teach it or support doesn't mean that you have ANY connection to Obama. There is no conspiracy.

And classics in literature? It's full of them. It just includes more recent empowering texts, also. Literature students may read the Preamble and also the lyrics to a popular song. Maybe an excerpt from Moby Dick and maybe an excerpt from The Hunger Games.

And only teaching basic geometry? Maybe in 3rd grade, but not in upper grades. The math is tougher in respects to it's requiring students to dig deeper into the why and how's of mathematics and removing itself from rote formulaic exercises. You still have to give evidence that you CAN manipulate numbers rotely, but that's no longer emphasis and actually hasn't been in public school long before common core - but now even more so.

For example, my 7th grade class is working on rates, proportions, and unit rates. They have to manipulate these ideas with complex fractions, percents, charts, verbal clues, coordinate plans, algebraic equations, scale drawing, and more - all in real-world applications.

Nothing fuzzy about it.

In fact, here is a link to some common core material. View it for yourself.

Look at the sample planning. When it says sample, it just means the order of the units is a suggestion. All of the content is rigid and fixed.

http://www.louisianabelieves.com/resources/library/year-long-scope-sequence

Feel free to ask questions, give an opinion, or rip what I do to shreds AFTER you've looked at the actual data.

 

[thisnumbersdisconnected]

Scarlett, just one question ...

Does your school system teach the multiplication tables?

 

[Scarlett O.]

Scarlett, just one question ...

Does your school system teach the multiplication tables?

Yes, in 2nd and 3rd grades. They are supposed to have them all memorized (sometimes up to the 15's) by middle of 4th grade, but without parent help from home, it's very hard for some students.

 

[Revmitchell]

I don't have much time say anything except that this "report" by Fox News (which I typically enjoy) is not credible.

I am a little concerned about this statement. The report makes no claims it only reports what claims are being made about the testing. The reporting is very credible, whether or not the criticism made by others is credible is not the same thing.

However, I have a question of you, is the following statement true of this testing:

So 3 times 4 can now equal 11 so long as a student can effectively explain how they reached that answer.”

 

[thisnumbersdisconnected]

Yes, in 2nd and 3rd grades. They are supposed to have them all memorized (sometimes up to the 15's) by middle of 4th grade, but without parent help from home, it's very hard for some students.

Then your schools there are an exception to a hugely disappointing trend. Without the multiplication tables, all math is fuzzy. The standard program for math in our schools since about 1966 has been to teach "math facts" without the old-time, tried-and-true rote method of memorizing the multiplication tables. Yours is the first school system I've heard of in years that actually teaches them.

 

[Crabtownboy]

Then your schools there are an exception to a hugely disappointing trend. Without the multiplication tables, all math is fuzzy. The standard program for math in our schools since about 1966 has been to teach "math facts" without the old-time, tried-and-true rote method of memorizing the multiplication tables. Yours is the first school system I've heard of in years that actually teaches them.

Fuzzy math is a credible area of mathematics. Maybe you do not know that.

Fuzzy mathematics forms a branch of mathematics related to fuzzy set theory and fuzzy logic. It started in 1965 after the publication of Lotfi Asker Zadeh's seminal work Fuzzy sets.[1] A fuzzy subset A of a set X is a function A:X→L, where L is the interval [0,1]. This function is also called a membership function. A membership function is a generalization of a characteristic function or an indicator function of a subset defined for L = {0,1}. More generally, one can use a complete lattice L in a definition of a fuzzy subset A .[2]
The evolution of the fuzzification of mathematical concepts can be broken down into three stages:[3]
1.straightforward fuzzification during the sixties and seventies,

2. the explosion of the possible choices in the generalization process during the eighties,

3. the standardization, axiomatization and L-fuzzification in the nineties.

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

 

[thisnumbersdisconnected]

Fuzzy math is a credible area of mathematics. Maybe you do not know that.

Or maybe I refuse to accept the word of even the most intelligent of mathematics geniuses when they try to tell me that it is "credible" or logical to accept a theory that claims there do not have to be any right answers. Such is your so-called "credible area" of math.

Fuzzy math differs from conventional math primarily in the area of set theory. For example in a conventional "AND" statement both statements must be true for the statement to be true. However, in fuzzy logic, statements are not always true or false, they merely have varying levels of confidence. This is nothing more than an effort to affirm in the minds of our students that it is acceptable not to have an answer, for there to be no absolutes, that what you think is right is actually right.

This kind of math confuses the student and makes absolutely no sense whatsoever. Engineers and scientists are being told there are applications in fuzzy mathematics for their areas of specialty. It isn't math. It's philosophy. This kind of math didn't get us to the Moon. Ridiculous. Therefore, it is ...

And ... Really?? A WikiPedia citing?

 

[Revmitchell]

Nothing credible about intentionally avoiding absolutes. The corruption of post modernism.

 

[Don]

Fuzzy math is a credible area of mathematics. Maybe you do not know that.

Perhaps in theoretical physics, which is where I first learned of "Fuzzy Math" back around 1999...but it has no place in business or "every day" math.

 

[Revmitchell]

Perhaps in theoretical physics, which is where I first learned of "Fuzzy Math" back around 1999...but it has no place in business or "every day" math.

Or in basic math testing in our schools. I am still trying to figure out why old Bill thought that was relevant.

 

[Don]

Or in basic math testing in our schools. I am still trying to figure out why old Bill thought that was relevant.

Please note that I was responding to CTB, not Scarlett.

 

[Revmitchell]

Please note that I was responding to CTB, not Scarlett.

I understood that.

 

[Scarlett O.]

Hey Rev.

About this quote you found...

So 3 times 4 can now equal 11 so long as a student can effectively explain how they reached that answer.”

This is not an accurate portrayal of math today in common core or even yesterday in a former curriculum. The author of this quote is either misinformed or has an agenda of some kind.

Here's an explanation:

[1] The fundamental truths of math can never change. 3 x 4 will always be 12. The quadratic equation never change nor will the formula for finding the area of a circle. Absolute truths cannot change.

[2] There IS a leaning toward more of a investigative approach to math, but ONLY in regards of investigating to discover the truth or what makes the truth true - SO THAT the truth will be more meaningful to the student, ergo causing deeper understanding that can be connected to other truths. (Did that confuse you, LOL!)

For example. Yes, 2 x 8 = 16. So does 8 x 2. And 4 x 4, which can be called 4 squared.

What a teacher might do in introducing multiplication facts and in introducing square numbers is to teach an array.

She might have the kids draw a two rows of circles with 8 circles in a row and then she might draw on the board 8 rows of circles with two in each row. Once she explains what multiplying is and they discuss why their array and HER array actually mean the same thing - even though they look different - she then can lead them into understanding how 2 x 6 and 6 x 2 need to be learned as the same thing. You'd be surprised at small children who can't figure what 8 x 7 is, but if you ask them what 7 x 8 is - they know it every time.

Then she might show a picture of an array of 4 rows of circles with 4 circles in each row. She'll ask, "Is this array the same as mine and yours?" Naturally, they all say "No!" because it "looks" different.

Then she'll say, "Well, let's count them and see if we get 16."

When they see it's the same, THEN comes the investigation .... she'll ask, "Well.... how can all of these arrays be equal if they make different shapes and don't look the same to our eyes?"

And BOOM! There is it. All of sudden the little wheels begin to turn and little hands start to go up and all kinds of intelligent discussion of how there is more than one way to multiply numbers and get 16. And you have have an AMAZING discussion on what "equivalent" means.

Then when those same children get into 4th grade, they can add 32 x 1/2 and the square root of 256 to that idea of what "16" is.

I know that sounds so simple, but without investigation that leads to understanding the absolutes, some children only mimic behavior and can't "learn". They can't take a test alone. They can't do homework alone. They can't function without a calculator. They are constantly counting on their fingers.

Be rest assured. 3 x 4 is still 12. :thumbs:

 

[Magnetic Poles]

Fuzzy math is a very useful part of applied mathematics. We use it all the time in our everyday lives. To give one example, we may deem temperatures over 85 degrees Fahrenheit as a hot day (but it is also a cool oven). Temps between about 65 and 85 may be to some, a temperate day; between 50 and 65, chilly; and below 50, a cold day. Not all questions are seeking absolute answers, but the answers provided by fuzzy math can determine if you wear short sleeves, a sweater, or a heavy coat. Attempts at politicizing mathematics is just silly.

 

[Crabtownboy]

Or in basic math testing in our schools. I am still trying to figure out why old Bill thought that was relevant.

Rev. you are out of date. Catch up with the times.

The controversy over K-12 math education has come to be known as the “math wars.” Like Schmid, mathematicians have been active in this debate, as has the “mathematics community” at large, including not only mathematicians at the university level, but teachers and others involved in the education establishment. They believe that students must master basic skills (the number facts, standard algorithms for adding, subtracting, multiplying, and dividing) in tandem with larger concepts about mathematics.

On the other side of the debate are the followers of an education theory that promotes discovery learning, minimization of both teacher instruction and repetitive drills, and a disdain for standard procedures (algorithms). The math being protested–by the mathematics community–is called a variety of things: “reform math,” “standards-based math,” “new new math,” and, most commonly, “fuzzy math.”

http://educationnext.org/anamazeingapproachtomath/

 

[Bro. Curtis]

Fuzzy math is very useful. It's got the libbies convinced Obama does some pretty fine presidentin'.

 

[Revmitchell]

Hey Rev.

About this quote you found...



This is not an accurate portrayal of math today in common core or even yesterday in a former curriculum. The author of this quote is either misinformed or has an agenda of some kind.

Here's an explanation:

[1] The fundamental truths of math can never change. 3 x 4 will always be 12. The quadratic equation never change nor will the formula for finding the area of a circle. Absolute truths cannot change.

[2] There IS a leaning toward more of a investigative approach to math, but ONLY in regards of investigating to discover the truth or what makes the truth true - SO THAT the truth will be more meaningful to the student, ergo causing deeper understanding that can be connected to other truths. (Did that confuse you, LOL!)

For example. Yes, 2 x 8 = 16. So does 8 x 2. And 4 x 4, which can be called 4 squared.

What a teacher might do in introducing multiplication facts and in introducing square numbers is to teach an array.

She might have the kids draw a two rows of circles with 8 circles in a row and then she might draw on the board 8 rows of circles with two in each row. Once she explains what multiplying is and they discuss why their array and HER array actually mean the same thing - even though they look different - she then can lead them into understanding how 2 x 6 and 6 x 2 need to be learned as the same thing. You'd be surprised at small children who can't figure what 8 x 7 is, but if you ask them what 7 x 8 is - they know it every time.

Then she might show a picture of an array of 4 rows of circles with 4 circles in each row. She'll ask, "Is this array the same as mine and yours?" Naturally, they all say "No!" because it "looks" different.

Then she'll say, "Well, let's count them and see if we get 16."

When they see it's the same, THEN comes the investigation .... she'll ask, "Well.... how can all of these arrays be equal if they make different shapes and don't look the same to our eyes?"

And BOOM! There is it. All of sudden the little wheels begin to turn and little hands start to go up and all kinds of intelligent discussion of how there is more than one way to multiply numbers and get 16. And you have have an AMAZING discussion on what "equivalent" means.

Then when those same children get into 4th grade, they can add 32 x 1/2 and the square root of 256 to that idea of what "16" is.

I know that sounds so simple, but without investigation that leads to understanding the absolutes, some children only mimic behavior and can't "learn". They can't take a test alone. They can't do homework alone. They can't function without a calculator. They are constantly counting on their fingers.

Be rest assured. 3 x 4 is still 12. :thumbs:

Well this fella disagrees with you:

Stanford Prof. James Milgram, the only mathematician on the Common Core Validation Committee, refused to sign off on the math standards, calling the whole thing “in large measure a political document” during testimony he gave in May 2011 in which he advocated for Texas not to adopt the Common Core standards.
“I had considerable influence on the mathematics standards in the document. However, as is often the case, there was input from many other sources -- including State Departments of Education -- that had to be incorporated into the standards,” he said during the testimony.
“So three times four can now equal 11 so long as a student can effectively explain how they reached that answer.”
- Glyn Wright, Eagle Forum
“A number of these sources were mainly focused on things like making the standards as non-challenging as possible. Others were focused on making sure their favorite topics were present, and handled in the way they liked,” he also said, adding that it led to a number of “extremely serious failings” in the Common Core that made it premature for any state hoping to improve math scores to implement them and that the Core Math standards were designed to reflect very low expectations.


Read more: http://www.foxnews.com/us/2013/08/3...d-less-fiction/?intcmp=trending#ixzz2dz32dxTZ

 

[thisnumbersdisconnected]

Fuzzy math is a very useful part of applied mathematics. We use it all the time in our everyday lives. To give one example, we may deem temperatures over 85 degrees Fahrenheit as a hot day (but it is also a cool oven). Temps between about 65 and 85 may be to some, a temperate day; between 50 and 65, chilly; and below 50, a cold day. Not all questions are seeking absolute answers, but the answers provided by fuzzy math can determine if you wear short sleeves, a sweater, or a heavy coat. Attempts at politicizing mathematics is just silly.

And yet, on any given day, there is an exact, absolute high temperature, and an exact, absolute low temperature, is there not? And even though the high and low temperatures at Kansas City International, for example, are different from the highs and lows in downtown Kansas City, neither location experiences a "range of highs and lows" do they? No, they both have definite temps for each benchmark. If "fuzzy math" is so useful in this venue, as you claim, why in 1987 did NOAA abandon the practice of giving a potential range of highs and lows and start giving exact temps in their daily forecasts?

Fuzzy math is nothing more than an effort to affirm the agenda of those who want to force upon all of us the idea of relative truth. It is a political arena, not a mathematical one.

 

[Crabtownboy]

Fuzzy math is nothing more than an effort to affirm the agenda of those who want to force upon all of us the idea of relative truth. It is a political arena, not a mathematical one.

What an amazing statement! You really do not know that "fuzzy math" is real, is credible and has nothing to do with politics. That is simply amazing.

Here is the definition of "fuzzy math" from Dictionary.com

Main Entry: fuzzy math
Part of Speech: n
Definition: an approach to teaching mathematics without emphasis on rote learning and memorization but more on conceptual understanding; also called whole math, new new math

Rote memory is not the best way to teach any subject and especially math.