Another volley fired in the Math Wars: Seattle's Math Secret

[creekland]

I wish he had links since I tend to believe that drilling (in a variety of ways including some fun ones:)) is good for the mind and focusing.

 

His quote is agreeing with you. ;) I do too.

[wapiti]

Yeah, I don't like it either. However, we do not have to limit our choices of how to teach math to two bad extremes. "Fuzzy Math" and "Drill and Kill" are both imbalanced approaches.

 

...

Tragic. The answer is math education that develops deep understanding and the ability to do multi-step problem solving. A return to "we'll give you the numbers to plug into a provided formula" type math education is not a sufficient answer to the problem. It is not an option that should be on the table.

 

I don't know why there aren't more choices in the middle that offer the best of both rather than the worst. If I were a mathematician I'd write a curriculum :tongue_smilie:. This problem is seriously driving me crazy right now, though perhaps a curriculum can only do so much.

[creekland]

Absolutely. But none of the fuzzy math programs I'm familiar with even come close to doing this.

 

:iagree: BUT I'll admit to not knowing them all - or - at this point, caring to get more familiar with any of them.

 

Even Life of Fred... one homeschooled student had used that for Stats and it was part of his story on college confidential. He is now going to Stanford. He had gotten high scores on many AP tests, but not Stats. My guy used a traditional book, self studied and got a 5 without asking me more than 2 questions all year. It makes me think Life of Fred was lacking just a wee bit for Stats anyway.

[Spy Car]

I don't know why there aren't more choices in the middle that offer the best of both rather than the worst. If I were a mathematician I'd write a curriculum :tongue_smilie:. This problem is seriously driving me crazy right now, though perhaps a curriculum can only do so much.

 

I don't get it either. The home-school market is relatively fortunate to have a number of strong Third Way math programs for elementary school. The pickings are a lot slimmer in the public school world.

 

Even there things can go hay-wire. Yesterday I toured a charter-school here that uses Primary Mathematics (Singapore) and at every grade level (K-3rd) they were teaching the kids to count on their fingers. My head almost exploded! :D

 

Bill

[creekland]

 

Do math teachers in middle school have math majors or minors? Or are they like the elementary teachers who are often lacking in math skills? I agree with Creekland that a traditional program works best if the teacher is incompetent.

 

I used to think it was teacher incompetence and in some cases, I still think it is. However, I've been in a couple of classrooms while the teachers are still there. It isn't always the teacher. With apathetic kids (and most are in ps) these programs don't work. With good kids it still doesn't work as well as I'd like to see. I've had 6 years of watching it now - and as mentioned before - our top teachers (College Alg, Stats, Calc) are all saying the same thing - kids are poorly prepared coming in to their classes. It's not just me saying it. But... they haven't yet connected the dots to get the solution. A few have, but they don't get to make the decisions as don't I. I can be more vocal to a degree as I don't work there full time and I see literally ALL the classes at some point or another.

 

I see the kids in their science classes too. It's pathetic. What they are supposed to have in math skills don't carry over there either.

[creekland]

 

It is a problem because it plays into the (wrong) impression that the only choices are between hair-brained impractical math programs and algorithm-only "traditional" math. Neither are adequate for life in the 21st Century. As long was we lurch back and forth between bad options we will fall behind the rest of the world, and they will eat our lunch.

 

 

 

One could argue that the drill would be like a bandaid on a festering sore. It is insufficient to slap drill on top of fundamentally bad math education and think you've fixed the problem.

 

 

 

While it is necessary to score well on standardized tests the telling line here is that you were "not a confident math student." We should be aiming toward creating confident math students who see mathematics as a native language that they know inside and out.

 

 

 

Tragic. The answer is math education that develops deep understanding and the ability to do multi-step problem solving. A return to "we'll give you the numbers to plug into a provided formula" type math education is not a sufficient answer to the problem. It is not an option that should be on the table.

 

Bill

 

You know what, Bill? I fully agree with you on these points. ;)

[Sun]

...

Tragic. The answer is math education that develops deep understanding and the ability to do multi-step problem solving. A return to "we'll give you the numbers to plug into a provided formula" type math education is not a sufficient answer to the problem. It is not an option that should be on the table.

 

Bill

 

Bill, I'm pretty sure that Cliff Mass (the meteorology professor who writes the blog) would agree with you wholeheartedly. I've read other articles by him lamenting the state of math education in Washington state. I think his gripe is fueled by the lack of math proficiency that he sees in his university courses. This blog post discusses the results of a fairly basic math exam he administered to one of his classes. The results are pretty shocking since the test covers material that should be known by the end of middle school. A blank copy of the test is available there as well, if anyone wants to see it.

[T'smom]

Could someone define exactly what "fuzzy" math is?

[Sebastian (a lady)]

I wish he had links since I tend to believe that drilling (in a variety of ways including some fun ones:)) is good for the mind and focusing. Of course, I also believe in understanding and discovering concepts as well:) I truly believe that kids are capable of memorizing quite a bit and that it is useful.

 

Some educators make it seem like drilling only has to be killing a love of learning which is wrong IMHO. Drilling done properly along with teaching understanding and discovery can be great. Drilling can also be done in fun ways too as well as nitty gritty practice which also has great value. Humans relied on memory to pass on our histories and traditions for eons and now it is considered drill and kill???:001_huh:

 

I think that there are a lot of strawman arguments posed when you start talking about educational philosophy (math, history sequence, reading . . .)

 

It's easy to mock memorization as "drill and kill". But you can understand what multiplication is and still be hobbled unless you can quickly say that 7x8=56 or that 9x6=54.

 

At the same time, it is possible to learn what to do with a type of problem, but not understand why you are doing it. Dividing fractions or cross multiplication are favorite examples of mine. My kids sometimes forget why it works (ie, what longer steps that shortcut represents) and therefore can get caught up in making a mistake that they wouldn't make if they were thinking about the equation balancing they are doing.

 

We found Saxon to be a powerful tool. (More powerful when we made sure not to take shortcuts on lessons. :D) But we are also loving AoPS. And I never saw Saxon as being just an exercise in memorization. Our manipulatives, diagrams and thinking skills got lots of work.

 

And there was one comment I found about SMSG a couple weeks back that I thought was interesting. The author observed that at one point in time (early 1970s) about half of the upper level math teachers had attended on "institute" for teaching via "new math" methods. But that this exposure and math background did not extend to the elementary level, which contributed to the failure of the curriculum.

 

Unless we drastically change how elementary schools are organized, we will have to deal with classroom teachers who have to be generalists, knowing about teaching reading, math, science, etc. And as opportunities for women and minorities have opened up, teaching has become less of a prestige option for people who were formerly shut out of other job choices.

 

ETA: FWIW, my kids did 90% Saxon (with a little Singapore CWP and some Key to booklets when we traveled) until this year. The older two scored a 14 and a 15 on the AMC 8 exam, which put them in the top 25%. There are educational fashion trends in homeschooling just as in other education options. Nothing is a panacea. Nothing works for everyone. But I also think that Saxon gets more criticism than it warrants. (JMHO, YMMV)

Edited December 7, 2011 by Sebastian (a lady)

[FaithManor]

I don't get it either. The home-school market is relatively fortunate to have a number of strong Third Way math programs for elementary school. The pickings are a lot slimmer in the public school world.

 

Even there things can go hay-wire. Yesterday I toured a charter-school here that uses Primary Mathematics (Singapore) and at every grade level (K-3rd) they were teaching the kids to count on their fingers. My head almost exploded! :D

 

Bill

 

 

Bill, don't let it happen! Your family needs you! :D Preserve your brains for your son so you can make sure he doesn't fall through the cracks.

 

However, I do absolutely understand what you mean. The balanced approach is sooooooooo hard to find. I don't know why there have to be these extreme pendulums in curriculum.

 

Something has to give. The manufacturing jobs in this country are gone. Everything is becoming more technologically, scientifically advanced. If we want to remain an advanced society, then education needs to do more than assume there will always be a good, high paying but low-functioning-in math-and-science job available. We don't have it in this state. It's especially bad here because with the unemployment rate is so high, that the average kid who is still practically counting on his fingers upon exiting high school is competing with retired folks for a job bagging groceries, with degree folk, and those with LOTS of work experience just for a job at McDonalds, etc. and those jobs that could have paid well if you bided your time, worked up the ladder, took your on-the-job training, etc. aren't there anymore either because people with advanced training are out of work and snapping them up. Even the military is more discerning of whom they recruit. The educational system has to get it's head out of the hole and take a look around. We don't have 10 years for it to figure out that what it is doing is wholly inadequate.

 

Okay, my rant is off. My 14 year old has just presented me with a fine algebra assignment, beautiful graphs, and a wonderful verbal explanation of how his story problems were solved and under what circumstances he would need a different approach to solving a similar problem. I'm wallowing in "math contentment" at the moment so it's supremely easy to snarl about the school down the road! :D

 

Faith

[Perry]

A return to "we'll give you the numbers to plug into a provided formula" type math education is not a sufficient answer to the problem. It is not an option that should be on the table.

 

Bill

But is anyone really advocating that? I think most people are in agreement that you have to be able to understand what you're doing. What people are so angry about is the open hostility towards mastery in fuzzy math curricula.

[NoPlaceLikeHome]

But is anyone really advocating that? I think most people are in agreement that you have to be able to understand what you're doing. What people are so angry about is the open hostility towards mastery in fuzzy math curricula.

 

:iagree: I would never dream of doing math without understanding:).

[stripe]

I wish he had links since I tend to believe that drilling (in a variety of ways including some fun ones:)) is good for the mind and focusing. Of course, I also believe in understanding and discovering concepts as well:) I truly believe that kids are capable of memorizing quite a bit and that it is useful.

 

 

I agree with you; I also think, in the age of being worried about self-esteem, children feel good about themselves when they actually know about things and how to do things.

 

I wrote a post about a book called Brain that Changes Itself by Norman Doige here. The author felt very strongly that practicing neat handwriting, poetry memorization, and careful pronunciation (all being valued in classical education but more recently seen as boring) built up the brain, and in fact often helped "lesser" students succeed.

[Leav97]

The district we *would* be in has a similar approach to math, and over the years, every last parent I know has had to pay for math tutoring for their kids so they could learn the basics. That is lovely that they can *afford* to do this...but where does it leave the kids whose parents cannot afford math tutoring. .

 

Here's the additional complication of this. When the test scores don't decrease (because parents are paying to make sure their kids don't suffer) the administration can claim success. It makes for a spiral of frustrated parents.

[Spy Car]

But is anyone really advocating that? I think most people are in agreement that you have to be able to understand what you're doing. What people are so angry about is the open hostility towards mastery in fuzzy math curricula.

 

Yes, I think most of the reactionary parent groups that are protesting (with cause) against "fuzzy math" programs are happy enough to return to "procedure-only" type math education.

 

"Procedure-only" may be a slight over-statement, but it is back to the sort of math education that teaches "invert and multiply" without any real understanding of the mathematics. We are not at a point in our nation's history when we can go back to shallow math education, and "fuzzy math" is clearly not the answer either. We need a Third Way.

 

Bill

[Perry]

Yes, I think most of the reactionary parent groups that are protesting (with cause) against "fuzzy math" programs are happy enough to return to "procedure-only" type math education.

 

"Procedure-only" may be a slight over-statement, but it is back to the sort of math education that teaches "invert and multiply" without any real understanding of the mathematics. We are not at a point in our nation's history when we can go back to shallow math education, and "fuzzy math" is clearly not the answer either. We need a Third Way.

 

Bill

The reform math people certainly would have you believe this, but it's a misrepresentation. When my oldest was just starting elementary school, I organized a community group for parents interested in math ed. I created a website and communicated with numerous parent groups across the country, including the folks at Mathematically Correct, NYC Hold, and Illinois Loop. It was clear that no one was looking for "procedure only" math, and it infuriated them that that was how they were characterized.

 

OTOH, there is a lot to be said for practice and drill. Many of the concepts I learned in grad school I only fully understood after doing problems repeatedly. The concepts had been fully explained, but they were difficult and for most people, a true understanding only develops after many, many repetitions.

[creekland]

Here's the additional complication of this. When the test scores don't decrease (because parents are paying to make sure their kids don't suffer) the administration can claim success. It makes for a spiral of frustrated parents.

 

And this is what is happening here. The few "good" students at our school are being held up as examples of what can happen with our curriculum. It doesn't matter if they had to do tons outside of school to get there.

[Spy Car]

The reform math people certainly would have you believe this, but it's a misrepresentation. When my oldest was just starting elementary school, I organized a community group for parents interested in math ed. I created a website and communicated with numerous parent groups across the country, including the folks at Mathematically Correct, NYC Hold, and Illinois Loop. It was clear that no one was looking for "procedure only" math, and it infuriated them that that was how they were characterized.

 

OTOH, there is a lot to be said for practice and drill. Many of the concepts I learned in grad school I only fully understood after doing problems repeatedly. The concepts had been fully explained, but they were difficult and for most people, a true understanding only develops after many, many repetitions.

 

I don't know Perry. I'm not a "reform math" person (quite to the contrary) and I've read numerous articles on anti-reform math websites for my own self and I don't see it as a mischaracterization.

 

The linked article is pretty typical it seems to me.

 

Bill

[stripe]

Not to sound cynical, but...

 

Are there really that many kids who even have metely memorized a bunch of procedures? I don't generally meet non-mathy people who even know when or what to "invert and multiply."

 

What I see is mostly those for whom, evidently, nothing stuck. Look at all the people who just don't grasp credit card and other debt. I saw a man on Oprah with Suze Orman who thought he'd be paying off his enormous (>$10,000) credit card debt in two years by merely making the monthly payment. Ignoring interest completely, how does $15 per month for 2 years add up to tens of thousands of dollars?

[FaithManor]

Yes, I think most of the reactionary parent groups that are protesting (with cause) against "fuzzy math" programs are happy enough to return to "procedure-only" type math education.

 

"Procedure-only" may be a slight over-statement, but it is back to the sort of math education that teaches "invert and multiply" without any real understanding of the mathematics. We are not at a point in our nation's history when we can go back to shallow math education, and "fuzzy math" is clearly not the answer either. We need a Third Way.

 

Bill

 

 

Absolutely Bill! I think my posts have made clear that I am a. against the concept that no drill needs to take place and no memory work, but am not the extreme b. it should be only about HOW math works. I am no fan of extremes.

 

My children are not educated by drill/ kill and procedures only nor are they only given the how and why of mathematics. They are given BOTH, in a blend so that they can compute well and do not, in the absence of a calculator, have to take their shoes off and begin using their toes as well as their fingers :D, but understand the pure mathematics, the theory, the how a formula works, how it was derived, how it can be applied to real life. I want them to plug numbers into a calculator in high school and understand why they have the answer they have gotten and how that number can be used in practical application (dh majored in pure mathematics in college so you can bet, they get an awful lot of "the beauty, the elegance, of mathematics). THAT is what I want our schools to teach. But, for those that may have a learning disability or just not have enough background before arriving at school to make this an easy probability for them, I am still all for them being able to give me the answer to 6x8 off the top of their heads in a reasonable time frame without needing a calculator or a sheet of paper and pencil in which they draw six circles, put eight x's in each one, and then proceed to count x's one at a time. (Though I have to say, if the child knew to do even that much, it would be an improvement over the young man I tutored last week who literally had no clue to do even that! He is in 5th grade.)

 

Of course, I do appear to be living in dream world! After all, the youngest third grade teacher, when I asked of her if multiplication is an extension of addition or subtraction, her reply was, "Neither. The two aren't related."

 

We don't need just arithmetic and we do not need just mathematics, we need competency in both!

 

Faith

[Perry]

The linked article is pretty typical it seems to me.

 

Bill

I went back and read the article again, and I must be dense, because I'm not seeing how that would be considered a desire for procedure only math. He praises Saxon as "traditional" and "direct instruction" but there is plenty of concept development in Saxon. It's not my favorite curriculum, but there's good research that it's effective.

 

If it is his use of the term "discovery" math that you don't like, I really think that's shorthand for "the crappy reform math curricula in use in most American schools". Although in general, I don't believe that most discovery math curricula would be a good idea in a school setting. It's very inefficient if you're trying to teach a group, and it's a disaster in the hands of a teacher that doesn't have a good math background.

[Spy Car]

I went back and read the article again, and I must be dense, because I'm not seeing how that would be considered a desire for procedure only math. He praises Saxon as "traditional" and "direct instruction" but there is plenty of concept development in Saxon. It's not my favorite curriculum, but there's good research that it's effective.

 

He praises both Saxon for being "traditional" (which it is) and Singapore for being "traditional" (which made both Moira and I snicker).

 

I would be bummed to have my school math choices be between Everyday Math (or similar) and Saxon.

 

If it is his use of the term "discovery" math that you don't like, I really think that's shorthand for "the crappy reform math curricula in use in most American schools".

 

Yea, that bothers me because that is not what "discovery math" is. He is spreading nonsense, and it is a damaging kind of loose talk. There are some great discovery math programs, and I'm not at all sure EM and the like qualify as "discovery math" in any case. As I said earlier this creates collateral damage.

 

Although in general, I don't believe that most discovery math curricula would be a good idea in a school setting. It's very inefficient if you're trying to teach a group, and it's a disaster in the hands of a teacher that doesn't have a good math background.

 

Think discovery math methods like those used in Miquon could be extremely successful in early math education programs in schools. I have to disagree on that point while granting the second. A bad teacher can screw any program up.

 

Bill

[Lang Syne Boardie]

I've often thought our dear Maria Miller might hold the key.

 

Math Mammoth is affordable, easy to understand, user-friendly, and even comes with useful extras such as cumulative tests, extra worksheets, and computer games.

 

MM has a greater emphasis on mathematical concepts than we're used to, but doesn't skimp at all on mastery of facts, familiarity with new and traditional algorithms, or word problems.

 

I've always been very competent in traditional (American) math, and I've never had any trouble helping my dc with the Math Mammoth style. I think good public school teachers would find that they didn't need much training to teach with MM. It is different, but sensible and intuitive.

 

Another bonus: Because the instructions and teaching are directed to the student on the student pages, more parents would be able to help their children with homework.

 

Are there any schools using Math Mammoth yet?

[wapiti]

I've often thought our dear Maria Miller might hold the key.

 

Math Mammoth is affordable, easy to understand, user-friendly, and even comes with useful extras such as cumulative tests, extra worksheets, and computer games.

 

MM has a greater emphasis on mathematical concepts than we're used to, but doesn't skimp at all on mastery of facts, familiarity with new and traditional algorithms, or word problems.

 

I've always been very competent in traditional (American) math, and I've never had any trouble helping my dc with the Math Mammoth style. I think good public school teachers would find that they didn't need much training to teach with MM. It is different, but sensible and intuitive.

 

Another bonus: Because the instructions and teaching are directed to the student on the student pages, more parents would be able to help their children with homework.

 

Are there any schools using Math Mammoth yet?

 

I don't know whether there are any schools using it yet, but one of my dc is using it in his montessori classroom (long story; teacher likes it!! though she's mathy) and I also donated it to my other dc's classroom (though I have a feeling that teacher hasn't looked at it yet). I'm trying to convince the school to use it for the upper elementary grades because they are in the process of choosing a curriculum.

[nmoira]

I don't know whether there are any schools using it yet, but one of my dc is using it in his montessori classroom (long story; teacher likes it!! though she's mathy) and I also donated it to my other dc's classroom (though I have a feeling that teacher hasn't looked at it yet). I'm trying to convince the school to use it for the upper elementary grades because they are in the process of choosing a curriculum.

I have a friend who teaches elementary and uses MM as a supplement for kids who finish lessons quickly and would like more. I've heard some good things from her about PPS's new K5 program, Bridges in Mathematics, (at least compared to the old program) but that's the extent of my knowledge... I haven't had a chance to grill her yet. :tongue_smilie: A local non-profit developed it, and beat out Pearson, whose Investigations was the incumbent program.

[Sebastian (a lady)]

I have a friend who teaches elementary and uses MM as a supplement for kids who finish lessons quickly and would like more. I've heard some good things from her about PPS's new K5 program, Bridges in Mathematics, (at least compared to the old program) but that's the extent of my knowledge... I haven't had a chance to grill her yet. :tongue_smilie: A local non-profit developed it, and beat out Pearson, whose Investigations was the incumbent program.

 

The mention of Pearson reminded me of the tension that has to result from the differing goals of people in the textbook and education arena. A textbook company exists to sell books and support material. If they can promote changing fashions or automatically outdated items (like electronic content that is only good for a few years before needing to be repurchased), they can sell more stuff.

 

It really doesn't do a textbook company much good to say that they have a great program that teaches students well and is easy to implement that is also pretty durable and won't need to be constantly updated. Might work for a couple years, but then sales would drop.

[nmoira]

The mention of Pearson reminded me of the tension that has to result from the differing goals of people in the textbook and education arena. A textbook company exists to sell books and support material. If they can promote changing fashions or automatically outdated items (like electronic content that is only good for a few years before needing to be repurchased), they can sell more stuff.

 

It really doesn't do a textbook company much good to say that they have a great program that teaches students well and is easy to implement that is also pretty durable and won't need to be constantly updated. Might work for a couple years, but then sales would drop.

 

But, but, textbook publishers would be remiss not to keep up with advances in elementary mathematics. ;)

 

Teacher input was a critical here for PPS's moving away from Investigations. Bridges was field tested for, I think, four months, and the teachers using it overwhelming recommended it over Investigations.

[Sebastian (a lady)]

Sort of reminds me of a review of Latin for Americans that I was reading on Amazon. Now I'll start with the caveat that the reviewer was speaking from her experience as a Latin classroom teacher, experience I don't have. But to complain that the students were offended at the title (as if American's need dumbed down instruction was the complaint - which ignores both the specifics of American vocabulary and pronounciation and the fact that Americans often don't have strong grammar backgrouns) or that it felt too outdated because one chapter mentioned the Cold War struck me as really shallow.

 

A book that has good technique ought not lose its value just because the pictures are in black and white or it references older events or the people in the pictures have big hair. Or because the exercises use student names that don't reflect the school's student body (as was one complaint against Saxon a decade ago).

 

But then I'm cheerfully using a math text from 1965 alongside my Saxon, and my 4th grader begs for more of it because he likes how much it makes him think. I also have been scavenging for old (1965-1989) editions of our literature series while passing up on the newer editions (which are just horribly truncated and flighty). We're freaky book people here, and I'm not afraid to say it.

[Teachin'Mine]

Those on the high school boards will know that I seldom keep Saxon a secret. :D

[Riverland]

nm