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**Media and Inspiration / Fuzzy Math? **

« **on:**March 04, 2008, 12:02:04 am »

This is split from

One should be wary of small Wikipedia articles like this that cite no sources. I believe this is referring to the

I believe the actual 1989 document is

Now, I don't know what data they were looking at, and it's possible that they completely misread it. However, I'm also certain that this would be taken as "dumbing down" because they're teaching fractions later -- by people who have absolutely no idea about the research behind their claims.

In my (admittedly limited) teaching experience, one of the most eye-opening parts was seeing solid research being done into how well different educational strategies worked, rather than just arguing over anecdotal evidence of what different teachers liked.

Personally, I constantly see candidates who are able to give memorized answers to rote questions, but unable to critically consider and solve practical problems presented as such. As far as candidates go, I consider this to be a far more pressing problem than not knowing their times tables or other memorized facts. And I have often seen skilled physicists or engineers mess up on basic arithmetic, and as far as I can tell it doesn't correlate with their overall ability.

Now, I suspect your answer will be that the "fuzzy math" recommendations of the 1989 report have nothing to do with developing critical thinking, and are instead completely brain-dead nonsense with the teacher never giving any instruction to the students. There may well be bad teachers, but as far as I can see there's nothing in the report to encourage such.

**John Morrow's post on "Fuzzy Math"**in the thread**"Which game has the most rabid haters/critics?"**Quote from: John Morrow

Then there is Whole Math a form of child abuse (along with its equally evil twin, Whole Language):

It emphasizes word problems and understanding the concepts behind mathematical operations, rather than necessarily getting the right arithmetic answers for these operations. It has been widely used in the United States - particularly in California - since 1989, when the National Council of Teachers of Mathematics released standards that recommended children be taught the ideas behind math, versus focusing on calculation.

One should be wary of small Wikipedia articles like this that cite no sources. I believe this is referring to the

**Curriculum and Evaluation Standards for School Mathematics**published around 1989 by the National Council of Teachers of Mathematics. For example, that Wikipedia article suggests that fuzzy math was used "particularly in California". However, the more detailed and referenced Wikipedia article on**Reform Mathematics**states:*While the standards were widely and nearly universally adopted by the mid-2000s, at the same time many schools, school districts and even states such as California effectively rejected the standards, instead adopting rigorous traditional content and skill based standards and supplementing or replacing standards based curricula with Saxon math and Singapore Math.*I'm not sure which of these is correct, but as a parent in California with a son in public schools, I've never seen anything resembling what the fuzzy math article claims. My son has learned his additional and times tables just fine.I believe the actual 1989 document is

**available in PDF**from the Institute of Educational Sciences of the Dept. of Education. I just read it, and it seems pretty reasonable. Most critically, it frequently cites research into the results of teaching strategies. Here's a sample from the report:Quote

In addition to de-emphasizing complex pencil-and-paper computational operations, some traditional algorithmic skills are recommended to be developed later in the students coursework. This deferment is in order to support a better fit between childrens' developmental readiness for instruction and to allow for more time for maturation of conceptual understanding to precede skills acquisition.

Operations with fractions, for example, are one of the few areas where American students do relatively well on international comparisons in the early grades. However, this seems less attributable to better instruction than to the fact that other countries tend to teach these skills later in the curriculum. The year fraction operations are introduced, their students immediately jump ahead of American students -- presumably based on the laying of a sound conceptual base in the earlier years. Conversely, operations involving multi-digit addition and subtraction tend to be introduced later in the U.S. curriculum.

Now, I don't know what data they were looking at, and it's possible that they completely misread it. However, I'm also certain that this would be taken as "dumbing down" because they're teaching fractions later -- by people who have absolutely no idea about the research behind their claims.

In my (admittedly limited) teaching experience, one of the most eye-opening parts was seeing solid research being done into how well different educational strategies worked, rather than just arguing over anecdotal evidence of what different teachers liked.

Quote from: John Morrow

"In a typical fuzzy math class, children are placed in small groups, and encouraged to develop their own methods of solving arithmetical problems, presented in sentence format." And, remember, that it's not important that they get the right answer, just that they invent their own methods to solve the problem. Yeah, I want to fly in an airplane designed by one of these kids when they grow up. :rolleyes:

We wouldn't want to require kids to get the right answers or learn grammar or anything. That might hurt their fragile self-esteem. And, yes, they are really teaching kids this way in schools.

Personally, I constantly see candidates who are able to give memorized answers to rote questions, but unable to critically consider and solve practical problems presented as such. As far as candidates go, I consider this to be a far more pressing problem than not knowing their times tables or other memorized facts. And I have often seen skilled physicists or engineers mess up on basic arithmetic, and as far as I can tell it doesn't correlate with their overall ability.

Now, I suspect your answer will be that the "fuzzy math" recommendations of the 1989 report have nothing to do with developing critical thinking, and are instead completely brain-dead nonsense with the teacher never giving any instruction to the students. There may well be bad teachers, but as far as I can see there's nothing in the report to encourage such.