NYT "Math Wars" article

[wapiti]

FWIW....... http://opinionator.blogs.nytimes.com/2013/06/16/the-faulty-logic-of-the-math-wars/

[La Texican]

I'm just a mom not a professional teacher (and my oldest is only five, so I'm new) but I agree with the concept of the Bedtime Math website. Children become literate because we read them bedtime stories. We should do the same with numbers and they will be comfortable with math. I also agree with TWTM book that assigning extra practice is not enough when you should be teaching. I don't know anything much about progressive math (discovery math?). I guess it's like unschooling in that you're acting like a guide and strewing knowledge for the kids to discover. I don't know if it's my teaching or my kids learning style but I tried using objects, beads, coins and such for numbers but my kid seemed to understand it better with pencils and papers and dots, dashes, and circles the way that Khan Academy teaches. Singapore Math, Beast Academy, Khan Academy are all pretty popular. Which side of the math war are they considered to be on?

[wapiti]

Singapore Math, Beast Academy, Khan Academy are all pretty popular. Which side of the math war are they considered to be on?

 

They're not really involved in the math wars - the math wars are fuzzy math vs. traditional math, with each at the extreme end of a continuum. Singapore tends to offer the best of both worlds, instructing on both concepts and procedures. BA is on a whole other level, way above the math wars, LOL... Khan, from what I vaguely recall a few years ago, leans rather procedural, though it's possible it may have changed since the last time I took a good look.

[NASDAQ]

Singapore Math is often considered to be a compromise here, but it's a favourite of the anti-reform math people, who often explicitly urge school districts to adopt it instead of MathLand/TERC/Everyday Math.

 

Reform Math gurus hate Khan Academy. Khan Academy is very traditional.

 

Beast Academy is not a player in the math wars. I don't know if it even markets to schools. Pedagogically, it's neither reform nor traditional, but it's also inappropriate for the average student in a classroom setting.

[dewdropfairy]

I'm not "math-y" (though my oldest son is). Which side are Saxon and TT on?

[NASDAQ]

I'm not very familiar with TT, but I think it's traditional. Saxon is very, very traditional and procedural. Saxon is probably the most procedural of the math programs available.

[PachiSusan]

I found this article very well written and even the comments below were respectful and informative.

[Spy Car]

I hate articles like this one with the passion of a thousand suns.

 

The authors—yet again—perpetuate the canard that we only have two choices:

 

1) Go back to an algorithm-only, procedurally based "traditional" math education (one they would like to redeem—quite unconvincingly—as the "progressive" option).

 

or

 

2) We must accept "reform math" programs like TERC and Everyday Mathematics as the only other alternative.

 

What a load of hooey!

 

How many us us know there is a more sound Third Way? Lots! (including the OP). But yet the article forces the same old false dichotomy of two bad options. Balderdash!

 

Primary Mathematics, Miquon, MEP, Math Mammoth, Math-in-Focus, RightStart, and Beast Academy are among programs that prove the lie of the agruement.

 

As long as we continue to argue between stupid choices, we reman locked in a dumb agruement, and one with only bad outcomes. Instead, we need to understand there are other options. And that one can teach for depth of understanding, promote mathematical reasoning, inductive logic and creative problem solving, while at the same time developing a high procedural competence in both the standard argorithms and mental math.

 

We know this, why not the so-called "math experts"?

 

Bill

[Jane in NC]

I hate articles like this one with the passion of a thousand suns.

 

The authors—yet again—perpetuate the canard that we only have two choices...

Bill, this was precisely my thought as I read this article.

 

Arithmetic is, I am afraid, a series of algorithms that must be mastered. But Mathematics is far more than arithmetic.

 

A student in a basic Calculus course will not succeed without the skill sets of arithmetic and algebra. Unfortunately Calculus is now being reduced in many classrooms to nothing more than a series of algorithms--a step up from algorithms previously learned. Herein lies my objection to common mathematical pedagogy. Mathematics relies on the proof. I do not expect young children to prove mathematical concepts, but young children can be taught to consider the patterns they see in math and whether those patterns lead to inferences. Essentially a foundation can be laid so that while learning the necessary algorithms and mechanics of arithmetic, students can develop reasoning skills.

 

The options should not be "kill and drill" or fuzzy math. I do not believe that mathematicians perpetuate this myth; rather, this seems to be a war among math educators.

 

Now off to read the comments...

[creekland]

I'm firmly in the "kids should know both" camp and have found (via years of teaching at our public high school) that the majority learns best when they learn the steps first and the reason for the steps second (but close in order - same lesson). When they muddle through trying to figure things out they tend to guess incorrectly (it is a guess, after all) and then something equivalent to the primacy effect takes over making them forever think that first way was the correct way - or was it - they never can remember AND they seldom have learned enough to truly "know" in order to make it solid.

 

When they learn the steps first, followed immediately by the "whys" then they get the "aha" moment I like to see and the knowledge tends to be far more secure.

 

SOME kids can then go on and make inferences to other things - things they haven't yet done (not science apps and other related things - all should be able to do that). These kids will make your future researchers and similar. It's what they are talented in, but it's a fallacy to assume all kids can end up doing that (well) in the same way we don't expect all to be able to write a great original novel.

 

In short, teach both, but teach correct steps first followed immediately by a solid understanding of the whys/proofs/concepts and be sure both are understood. If just steps are taught, memory will be fuzzy and steps will be forgotten or when to do steps will be forgotten. If students need to come up with concepts and steps themselves, most will flounder for a lifetime IF they get it wrong to start with.

 

And again, this is for the majority (for ps classroom situations where you need the majority to do well). There will ALWAYS be individual exceptions to the majority. When homeschooling, choose what works well for your student.

[Jane in NC]

A question arises for me. Why is it that we have been waging this war between the dichotomy as presented in mathematics but not other disciplines? Is there a camp among music educators who believes that exercises to build muscle memory should be abandoned because they are not creative? Are there foreign language educators who believe that students should discover grammar? Do chemistry teachers expect students to develop their own version of the periodic table?

 

When I first studied pottery, I did hand building in clay to get the feel for the material. When you sit at a wheel, physics will determine where the clay is going. A potter learns to manipulate the material creatively--after establishing a foundation based on sound principles of physics and chemistry (since one does not want the pot to burst in the kiln). Most disciplines are like this. Establish first principles, then get creative. A novice potter does not make a tea pot but this does not stop a novice from exercising creativity.

[Catherine]

Bill, this was precisely my thought as I read this article.

 

Arithmetic is, I am afraid, a series of algorithms that must be mastered. But Mathematics is far more than arithmetic.

 

 

 

Yes, it is, but what I understand better now that I've read and studied Knowing and Teaching Elementary Math, and taught Rightstart all the way through, is that even arithmetic is a subject worthy of serious study. American math programs have often reduced arithmetic to a series of algorithms, but taught well it is far more. Yes young students need to commit the tables to memory but in my experience this will only work well, and be useful to the student later, if the memorization is based on a good conceptual understanding. This is kind of intuitive for some students, and definitely not for others. And the better a math program does in engendering that kind of deep conceptual understanding, the better the student will be able to translate his or her grasp of arithmetical concepts to higher math.

[creekland]

Yes, it is, but what I understand better now that I've read and studied Knowing and Teaching Elementary Math, and taught Rightstart all the way through, is that even arithmetic is a subject worthy of serious study. American math programs have often reduced arithmetic to a series of algorithms, but taught well it is far more. Yes young students need to commit the tables to memory but in my experience this will only work well, and be useful to the student later, if the memorization is based on a good conceptual understanding. This is kind of intuitive for some students, and definitely not for others. And the better a math program does in engendering that kind of deep conceptual understanding, the better the student will be able to translate his or her grasp of arithmetical concepts to higher math.

 

 

What I have seen come up from fuzzy math in our elementary/middle school are students who know how to use calculators well. They know all the buttons to push and can use them to follow steps.

 

What they are missing is any understanding of the concepts. If they accidentally push a wrong button they have no clue that their answer is way off base. An answer might need to be 3000. If the student gets 0.3 instead, they'll just assume that must be correct and move on.

 

The fuzzy math is supposed to teach concepts over memorization of tables/steps. It does neither for most students. It teaches steps and how to use a calculator. I've literally had students in "normal" classes not be able to do 4x2 or 2x100 without a calculator. Forget fractions.

 

Our school tests well for 8th grade math, but dies in Alg and higher. When kids do not actually know the math, they can't do higher level math well - and fuzzy math for higher level math gives an equal amount of knowledge (or lack thereof).

 

Pull the calculators from those 8th graders passing our state tests and our results would be absolutely dismal.

[Jane in NC]

 

What I have seen come up from fuzzy math in our elementary/middle school are students who know how to use calculators well. They know all the buttons to push and can use them to follow steps.

 

What they are missing is any understanding of the concepts. If they accidentally push a wrong button they have no clue that their answer is way off base. An answer might need to be 3000. If the student gets 0.3 instead, they'll just assume that must be correct and move on.

 

The fuzzy math is supposed to teach concepts over memorization of tables/steps. It does neither for most students. It teaches steps and how to use a calculator.

 

My son probably had a fair amount of Piaget exposure at his Montessori school. His conceptual understanding of mathematics came about because of his use of interesting manipulatives in a directed context. But this did not mean that he could avoid memorization or simple repeated practice of math facts. I used lots of games from Peggy Kaye's book to make things fun, but it was still practice.

 

I do see a third way here.

[AdventureMoms]

I think part of the problem is that it is very, very hard to teach math conceptually if one does not understand the concepts. In my experience, most elementary teachers do not understand math concepts very well. Not even those involved in basic arithmetic.

 

As others have said, I am also bothered by the false dichotomy. One can teach concepts and facts. Six years of elementary school is plenty of time to teach both the concepts and the facts of arithmetic. Which is not to say that "new math" teaches such a thing, but I do think concepts are important, even in algebra. It's a good thing to understand numbers as well as know how to manipulate them. And most people will be better manipulators of numbers if they understand the concepts.

[creekland]

I think part of the problem is that it is very, very hard to teach math conceptually if one does not understand the concepts. In my experience, most elementary teachers do not understand math concepts very well. Not even those involved in basic arithmetic.

 

As others have said, I am also bothered by the false dichotomy. One can teach concepts and facts. Six years of elementary school is plenty of time to teach both the concepts and the facts of arithmetic. Which is not to say that "new math" teaches such a thing, but I do think concepts are important, even in algebra. It's a good thing to understand numbers as well as know how to manipulate them. And most people will be better manipulators of numbers if they understand the concepts.

 

 

:iagree: I'll also add that I'm not convinced that many middle or high school math teachers understand the concepts well either... To truly know math one really needs concepts and facts - just as with any other subject really.

[AdventureMoms]

 

 

:iagree: I'll also add that I'm not convinced that many middle or high school math teachers understand the concepts well either... To truly know math one really needs concepts and facts - just as with any other subject really.

 

 

Agreed! Plus middle school and high school teachers can often be hired to teach a subject that might not have been their specialty. My high school physics teacher clearly had no inkling about math. And he was teaching 12th grade physics. I just happened to luck out and get very very good high school math teachers.

[AdventureMoms]

 

 

There are definitely differnces in opinions in other disciplines. Writing has been a big one. When I was a student we didn't start writing essays in 2nd grade. We weren't asked to fill page after page with invented spelling and our warm and fuzzy feelings when we were in first. Etc.

 

In music. I started off with one instructor and changed instructors. They had 2 completely different approaches. I bet they would have butted heads.

 

Reading has been another one. There is the whole sight word verses phonics debates.

 

 

Also in handwriting. Cursive or not? Cursive first or manuscript? Teach kids how to form letters in a specific way? Or except any letters that look like the correct letter?

[*Michelle*]

Agreed! Plus middle school and high school teachers can often be hired to teach a subject that might not have been their specialty. My high school physics teacher clearly had no inkling about math. And he was teaching 12th grade physics. I just happened to luck out and get very very good high school math teachers.

 

 

My geometry teacher lasted one year before moving to the phys ed department. Sucked to be in tenth grade that year. :glare:

[mom31257]

I find it hard to dislike traditional math teaching from years ago. My teachers always explained to us the "why" of the algorithms they were teaching us. I had 13 years of public school education and went on to make perfect math scores on my college entrance exams and obtain a BS in math. Many of the students in my school system went on to be doctors and engineers. We were prepared for what we needed to do in college and the real world.

 

Do you know how many young people I come across today who can't even give back correct change? Public education today is one big grand experiment that changes with the wind. The students are left behind to suffer in the wake of the mass hysteria driving top administrators and educators who are only out to make a name for themselves.

[UrbanSue]

Just to clear up some vocabulary (and, possibly, I am the one confused here). I've seen "discovery" used pejoratively in this thread. My understanding of "discovery" math is not that concepts and algorithms aren't taught but, rather, the student discovers them inductively. I was under the impression that the AoPS materials were on this model (and, from what I gather, that is a highly-regarded program) and I would describe Beast Academy that way as well. I learned geometry this way in school and it was the one year in high school where I actually learned something and excelled.

 

Someone asked if there are language programs where one is asked to "discover" grammar. We use Cambridge Latin which is a "whole to parts" or "reading" method and I might also describe it as a "discovery" approach. But the student isn't asked to invent something new. The student is taught the grammar. But generally the student has kind of figured it out already.

 

Perhaps I am the confused one and, if so, please educate me! But I have seen "discovery" used as a descriptor for a valid pedagogical approach in other places here. In this thread it seems to be attached to the "bad guys."

[mom31257]

 

Not sure how old you are, but that was not my experience. We were taught to memorize algorithms. That was it. There wasn't even mention of the concept of place value when I was in school. I remember asking my parents to buy me the largest box of crayons they could find so I could use them to do my math. LOL I didn't know what/why/how. I just counted my crayons.

 

 

I'm 46 and graduated high school in 1985. I just think it's a shame that education is evidently making it an either/or situation. Why can't the kids do a little exploring and a lot of practicing the algorithms? Why do they always have to be questioning traditional methods and demonizing them? What is wrong with teaching kids to do math accurately and precisely instead of creatively?

 

If I'm in a hospital needing the nurse to measure out some life-saving medication, I would rather know that she spent most of her time in math education practicing and perfecting the algorithms instead of years playing with manipulatives and doing math games to try and figure out solutions.

 

There is a time and place for the creative side of math, but most people in the real world will be better off knowing how to do the math they will need in their day to day lives.

[wapiti]

LOL, y'all were busy this morning... I'm just getting my coffee...

 

Just to clear up some vocabulary (and, possibly, I am the one confused here). I've seen "discovery" used pejoratively in this thread. My understanding of "discovery" math is not that concepts and algorithms aren't taught but, rather, the student discovers them inductively. I was under the impression that the AoPS materials were on this model (and, from what I gather, that is a highly-regarded program) and I would describe Beast Academy that way as well. I learned geometry this way in school and it was the one year in high school where I actually learned something and excelled.

 

Someone asked if there are language programs where one is asked to "discover" grammar. We use Cambridge Latin which is a "whole to parts" or "reading" method and I might also describe it as a "discovery" approach. But the student isn't asked to invent something new. The student is taught the grammar. But generally the student has kind of figured it out already.

 

Perhaps I am the confused one and, if so, please educate me! But I have seen "discovery" used as a descriptor for a valid pedagogical approach in other places here. In this thread it seems to be attached to the "bad guys."

 

 

You're right that the term discovery is commonly used to describe methods that are quite different.

 

The method of "discovery" in AoPS is literally *nothing* like the fuzzy math programs - couldn't be further. AoPS materials very carefully guide the student through the lesson by doing problems. In a Socratic sort of way, the sequence of lesson problems break down the lesson into tiny bits. Then, the full solutions for how the authors did the problems are presented, including mathematical properties, etc. (N.B.: as far as I know, only this board refers to the "discovery" angle of AoPS - that term does not come from the authors.)

 

In contrast, fuzzy math programs often involve wandering via group-think and one of the major criticisms of fuzzy math programs is that they never get around to showing the full solution - the how and why of the algorithm. Plus, they're usually super-spiral and fail to develop concepts in depth even though these programs supposedly lean conceptual.

[wapiti]

I'm not "math-y" (though my oldest son is). Which side are Saxon and TT on?

 

 

These traditional programs have a reputation for leaning heavily toward procedures/algorithms, a.k.a. plug-and-chug, but with less (for some students, potentially insufficient) emphasis on concepts and problem-solving - the opposite end of the spectrum from fuzzy math.

[EKS]

A question arises for me. Why is it that we have been waging this war between the dichotomy as presented in mathematics but not other disciplines? Is there a camp among music educators who believes that exercises to build muscle memory should be abandoned because they are not creative? Are there foreign language educators who believe that students should discover grammar? Do chemistry teachers expect students to develop their own version of the periodic table?

 

 

You see it in English classes. Grammar is not taught, usage is felt, comma placement aligns with natural pauses, academic writing instruction and assignments are replaced with journaling and short stories, classic literature is abandoned for that of the "young adult" variety.

[wapiti]

I find it hard to dislike traditional math teaching from years ago. My teachers always explained to us the "why" of the algorithms they were teaching us. I had 13 years of public school education and went on to make perfect math scores on my college entrance exams and obtain a BS in math.

 

 

I'm 46 and graduated high school in 1985.

 

 

I graduated high school in 1986 and can't complain about my elementary math education (except perhaps that it was much too easy). I often wonder whether I caught the tail-end of "New Math" in elementary in the 1970s, just enough of a focus on concepts. By late middle and high school in the 80s, I'd guess that the math I had was pretty traditional (most of my high school math teachers were pretty horrible, typical for my particular high school, so it's hard to say). The last math teacher I liked was my 7th grade prealgebra teacher who did some advocacy for me when I moved to a new district afterward, though oddly, I have zero recollection of having learned prime factorization. Ever. What is that about... it would have been so useful along the way. Was I looking out the window again or was I never taught? I want a do-over, LOL - I did very well on the math part of the SAT but I missed perfect by a smitch or two.

[Laura Corin]

Are there foreign language educators who believe that students should discover grammar?

 

I think the opposition made in foreign language is between osmotic/whole-to-parts learning and grammar-based parts-to-whole. I personally believe that the osmotic version works very well if there is the opportunity for true immersion; otherwise, parts-to-whole is more successful.

 

Laura (whose children learned spoken Chinese by immersion and French by parts-to-whole)

[creekland]

I find it hard to dislike traditional math teaching from years ago. My teachers always explained to us the "why" of the algorithms they were teaching us. I had 13 years of public school education and went on to make perfect math scores on my college entrance exams and obtain a BS in math. Many of the students in my school system went on to be doctors and engineers. We were prepared for what we needed to do in college and the real world.

 

Do you know how many young people I come across today who can't even give back correct change? Public education today is one big grand experiment that changes with the wind. The students are left behind to suffer in the wake of the mass hysteria driving top administrators and educators who are only out to make a name for themselves.

 

This was my high school too. It was great and prepared us well.

 

Unfortunately, as I know well after teaching at our local public high school for 14 years now (subbing, so seeing tons of different math/science classes), not all schools are equal no matter which type of math they choose to use. A good teacher can make a ton of difference with pretty much any curriculum. An average teacher plugs through with average results. A good curriculum helps here. A not-so-good teacher is a waste of time for most kids - then couple that with a not-so-good curriculum and :cursing: :nopity: . I had a young lady at the store the other day who couldn't figure out a price with my 99 cent competitor's coupon since she didn't have a calculator. It wasn't one of "mine" from school, but a similar age and experience in math.

[NASDAQ]

Regarding "procedural only"

 

The oldest math text I've worked is Wentworth's New School Arithmetic (originally 1898, my version 1904). It's sparse, as would befit a book from an era in which paper was expensive. The problem sets are on the long side. That said, it is no way "procedural" rather than "conceptual." Nor is it impractical and lacking connections to math in general life. An example :

 

 

40. A parenthesis preceded by the sign -. If a man with 10 dollars has to pay two bills,one of 3 dollars and one of 2 dollars, it makes no difference whether he takes 3 dollars and 2 dollars at one time, or takes 3 dollars and 2 dollars in succession, from his 10 dollars.

 

 

The first process is represented by 10 - (3 + 2)

 

The second process is represented by 10 - 3 - 2

 

 

Hence, 10 - (3 + 2) = 10 -3 - 2 (1)

 

 

If a man has 10 dollars consising of two 5-dollar bills, and has a debt of 3 dollars to pay, he can pay his debt by giving a 5-dollar bill and receiving 2 dollars.

 

 

This process is represented by 10 - 5 + 2

 

 

Since the debt paid is 3 dollars, that is, (5 - 2) dollars, the number of dollars he has left can be expressed by

 

 

10 - (5 - 2)

 

Hence, 10 - (5 - 2) = 10 - 5 + 2 (2)

 

 

If we use general symbols in (1) and (2) we have,

 

 

a - (b + c) = a - b - c

 

a - (b - c) = a - b + c

 

 

We have the general rule for a parenthesis preceded by -:

 

If an exp

ression within a parenthesis preceded by the sign -, the parenthesis may be remove,d provided the sign before each term within the parenthesis is changed, the sign + to - and the sign - to +.

 

 

I don't find that at all rote or "plug and chug." I think the rote, inflexible part comes about because teachers are insecure with the material.

[La Texican]

Just to clear up some vocabulary (and, possibly, I am the one confused here). I've seen "discovery" used pejoratively in this thread. My understanding of "discovery" math is not that concepts and algorithms aren't taught but, rather, the student discovers them inductively. I was under the impression that the AoPS materials were on this model (and, from what I gather, that is a highly-regarded program) and I would describe Beast Academy that way as well. I learned geometry this way in school and it was the one year in high school where I actually learned something and excelled.

 

Someone asked if there are language programs where one is asked to "discover" grammar. We use Cambridge Latin which is a "whole to parts" or "reading" method and I might also describe it as a "discovery" approach. But the student isn't asked to invent something new. The student is taught the grammar. But generally the student has kind of figured it out already.

 

Perhaps I am the confused one and, if so, please educate me! But I have seen "discovery" used as a descriptor for a valid pedagogical approach in other places here. In this thread it seems to be attached to the "bad guys."

 

 

I think I'm the only one that mentioned discovery math, and it wasn't perjoratively.

 

I don't know anything much about progressive math (discovery math?). I guess it's like unschooling in that you're acting like a guide and strewing knowledge for the kids to discover. I don't know if it's my teaching or my kids learning style but I tried using objects, beads, coins and such for numbers but my kid seemed to understand it better with pencils and papers and dots, dashes, and circles the way that Khan Academy teaches. Singapore Math, Beast Academy, Khan Academy are all pretty popular. Which side of the math war are they considered to be on?

 

 

It's only in parenthesis with a question mark because I was asking if what the article was calling progressive math was the same thing that the homeschool forum calls discovery math. I googled, "Is fuzzy math discovery math?" right after I posted here. Mr. Google says it is.

 

I think Right Start math, Hands on Geometry, Montessori manipulatives, Math u See (with Cuisanaire rods) are discovery. They are all highly recommended as quality products in threads around here.

 

In my experience, with my kid, he really seems to understand numbers and math just fine using a pencil and paper. I don't know if that's my teaching style or his learning style.

I was originally asking to clarify what the article was talking about and trying to rephrase it in common homeschool words. I should have asked Google, like I did right after. Yes, progressive math, discovery math, and fuzzy math seem to be the same as what's in the article.

[La Texican]

eta: he will happily draw out all the dots and circle groups to make division answers with remainders the way the Khan Academy video shows you how.

[La Texican]

 

 

You see it in English classes. Grammar is not taught, usage is felt, comma placement aligns with natural pauses, academic writing instruction and assignments are replaced with journaling and short stories, classic literature is abandoned for that of the "young adult" variety.

 

 

This is what I was trying to get at when I referenced the Well Trained Mind comment that "more practice isn't better, better teaching makes practice better." She wrote it about English classes assigning more practice instead of offering more instruction before assigning practice.

[La Texican]

oops., pushed the button twice

[UrbanSue]

I think I'm the only one that mentioned discovery math, and it wasn't perjoratively.

 

 

 

It's only in parenthesis with a question mark because I was asking if what the article was calling progressive math was the same thing that the homeschool forum calls discovery math. I googled, "Is fuzzy math discovery math?" right after I posted here. Mr. Google says it is.

 

I think Right Start math, Hands on Geometry, Montessori manipulatives, Math u See (with Cuisanaire rods) are discovery. They are all highly recommended as quality products in threads around here.

 

In my experience, with my kid, he really seems to understand numbers and math just fine using a pencil and paper. I don't know if that's my teaching style or his learning style.

I was originally asking to clarify what the article was talking about and trying to rephrase it in common homeschool words. I should have asked Google, like I did right after. Yes, progressive math, discovery math, and fuzzy math seem to be the same as what's in the article.

 

 

 

Someone else mentioned that it is fairly board-specific that some programs are called "discovery" here and it doesn't seem to mean quite the same thing. Now I know!

[wapiti]

It's only in parenthesis with a question mark because I was asking if what the article was calling progressive math was the same thing that the homeschool forum calls discovery math. I googled, "Is fuzzy math discovery math?" right after I posted here. Mr. Google says it is.

 

I think Right Start math, Hands on Geometry, Montessori manipulatives, Math u See (with Cuisanaire rods) are discovery. They are all highly recommended as quality products in threads around here.

 

In my experience, with my kid, he really seems to understand numbers and math just fine using a pencil and paper. I don't know if that's my teaching style or his learning style.

I was originally asking to clarify what the article was talking about and trying to rephrase it in common homeschool words. I should have asked Google, like I did right after. Yes, progressive math, discovery math, and fuzzy math seem to be the same as what's in the article.

 

 

Just to be clear for lurkers, a caveat on terminology: from what I can tell, the "progressive math" discussed in the article is indeed the same as "fuzzy math." It is true that "fuzzy math" is often known as "discovery math" (pejoratively and non-pejoratively). However, while Right Start, Montessori and MUS may involve some amount of discovery, none of those are what is referred to as "fuzzy math." Fuzzy math is a whole 'nother ball of wax.

[La Texican]

I just wanted to clarify that I was asking a question and not bad-mouthing something I have no experience with.

 

 

I just wanted to clarify that I was asking a question and bad-mouthing something I have no experience with.

[wapiti]

 

So what is Everyday Mathematics (besides a steaming hot pile of poo)? LOL

 

 

Fuzzy

[La Texican]

Just because an apple's a fruit, and an orange is a fruit, doesn't mean an apple's an orange. Got it. Fuzzy math is discovery math, but not all discovery math is fuzzy math.

[*Michelle*]

 

I'm 46 and graduated high school in 1985. I just think it's a shame that education is evidently making it an either/or situation. Why can't the kids do a little exploring and a lot of practicing the algorithms? Why do they always have to be questioning traditional methods and demonizing them? What is wrong with teaching kids to do math accurately and precisely instead of creatively?

 

If I'm in a hospital needing the nurse to measure out some life-saving medication, I would rather know that she spent most of her time in math education practicing and perfecting the algorithms instead of years playing with manipulatives and doing math games to try and figure out solutions.

 

There is a time and place for the creative side of math, but most people in the real world will be better off knowing how to do the math they will need in their day to day lives.

 

 

As an RN, I will tell you that we had many people fail out of nursing school because they didn't pass the required medication administration tests. Many. They were unable to figure out basic things like dosage calculation. Problems like "a correct dosage is 12.5mg/25 kg and the patient weighs 125 kg. How many milligrams should be given?" Then those people were livid because, after all, "the pharmacy figures that out for you anyway." I could hardly believe what I was seeing.