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

[nmoira]

http://cliffmass.blogspot.com/2011/12/seattles-math-secret-revealed.html

 

I don't think many here will be surprised by the "secret."

[Jean in Newcastle]

Unfortunately, I'm not surprised. I am ticked off at the superintendent's response, though.

[ErinE]

I'll don't think math programs based on discovery are necessarily the problem. Since using Miquon, I love the exploration it encourages for math concepts. However, I've also coupled Miqon with a SM spine to make sure we're covering the basics, because I know I'm not as talented a teacher as Lore Rasmussen. In the wrong hands, discovery math programs can be a great source of frustration for children. It requires strong guidance, lots of time, and a good understanding of the fundamentals. As a school district, you would need a deep pool of math teaching talent.

 

That being said, I find it appalling that a superindentent would be so married to her teaching philosophy that she would reject strong results on the basis it doesn't fit with her ideal pedagogy.

[UmMusa]

What a radical move on the school's part!

[kiana]

I'll don't think math programs based on discovery are necessarily the problem. Since using Miquon, I love the exploration it encourages for math concepts. However, I've also coupled Miqon with a SM spine to make sure we're covering the basics, because I know I'm not as talented a teacher as Lore Rasmussen. In the wrong hands, discovery math programs can be a great source of frustration for children. It requires strong guidance, lots of time, and a good understanding of the fundamentals. As a school district, you would need a deep pool of math teaching talent.

 

That being said, I find it appalling that a superindentent would be so married to her teaching philosophy that she would reject strong results on the basis it doesn't fit with her ideal pedagogy.

 

It requires a teacher who really, really knows what he or she is doing so that they can recognize when a student is working towards a valid discovery and when a student has made an invalid assumption. Furthermore, it takes more time to think through and discover and there's only so much time in the day.

 

Discovery math programs work better in suburban schools where the teacher likely knows math and the parents will rush the kids to Kumon if they need extra drill :P

[DarlaS]

It requires a teacher who really, really knows what he or she is doing so that they can recognize when a student is working towards a valid discovery and when a student has made an invalid assumption. Furthermore, it takes more time to think through and discover and there's only so much time in the day.

 

Discovery math programs work better in suburban schools where the teacher likely knows math and the parents will rush the kids to Kumon if they need extra drill :P

 

And it's got to be really helpful in a math program like that one, with so much discussion about concepts, if the kids speak English!

[kiana]

And it's got to be really helpful in a math program like that one, with so much discussion about concepts, if the kids speak English!

 

Hah. Yes. If the other students are talking and all the student hears is blah blah blah blah blah, it's not going to work so well :P

[Snickerdoodle]

Wow.

[....]

In the wrong hands, discovery math programs can be a great source of frustration for children. It requires strong guidance, lots of time, and a good understanding of the fundamentals.

 

:iagree: We also use discovery math and it's great when you are working one-on-one with your kid. However, I don't know how successful it would be in a classroom with 30 other kids. Also, you need to make sure they are still learning math facts, algorithms, etc. We also use Miquon and I plan to continue with AoPS.

 

Also, I think all discovery math programs are different. Last year, I saw our neighbor's daughter use Everyday Math. It looked nothing like what we do for discovery math.

[stripe]

I don't think many here will be surprised by the "secret."

 

I was hoping the secret was MEP!

[wapiti]

In our area, the regular public schools use primarily fuzzy programs - Everyday Math at our neighborhood elementary school; I'm not sure what our middle school uses (potentially something more traditional), but I know some of the other middle and high schools use a fuzzy program. In contrast, virtually ALL of the charter schools - and there are several - use Saxon (which, while far, far, far from my favorite, would be greatly preferable IMO to the fuzzy stuff). Oddly enough, I'm not aware of vast score differences, though I don't know what happens at the high school level.

 

This drives me crazy. Why does it have to be one or the other :banghead: , i.e., why isn't there something in the middle. (FWIW, I heard through the grapevine that the district experimented with a trial run of SM at one elementary school, and dropped it because the teachers apparently couldn't teach it :glare:.) Some of my kids are at a Montessori charter and the school is working on choosing curricula for upper elementary and the new middle school - you can bet I'm making noise about choices. (If you all see me posting next year about hs-ing more of my kids, you'll know how this all turned out :glare:)

[Elizabeth in WA]

I'm not at all surprised. I'm appalled by the math books used in my local district's "gifted" upper elementary school program and even more so in the regular elementary classes every time I help out with homework at an afterschool program associated with my kids TKD school.

 

While discovery can work really well, AoPS programs are fantastic, and I don't like Saxon elementary books, I do use upper level Saxon books because they work well for the way I run my homeschool. That is, for us, they are self-teaching with on the spot whiteboard demonstration and explanation by me as needed and provide sufficient review and practice without too much monotony in any one set. Formally taught, I would think they would be far more generally successful than the horrible books in use in middle and (upper) elementary schools near me.

[nmoira]

There's clearly much more going on in this school than just a change of math curriculum (see newspaper article linked in the blog post), and I'm not prepare to say that a particular curriculum is the best for all situations. The actual test scores mean nothing because the test itself decreased in difficulty, but what struck me was the relative (to the state average and to the higher SES schools) performance increases of poor, minority, and ESL students.

 

That the interim superintendent wasn't even interested enough to consider additional field trials is staggering.

[wapiti]

That the interim superintendent wasn't even interested enough to consider additional field trials is staggering.

 

This really makes one wonder about possible motivations. If I were the parents, I'd take it to the school board, which apparently would not be unusual in the math wars.

[NoPlaceLikeHome]

There's clearly much more going on in this school than just a change of math curriculum (see newspaper article linked in the blog post), and I'm not prepare to say that a particular curriculum is the best for all situations. The actual test scores mean nothing because the test itself decreased in difficulty, but what struck me was the relative (to the state average and to the higher SES schools) performance increases of poor, minority, and ESL students.

 

That the interim superintendent wasn't even interested enough to consider additional field trials is staggering.

I see what you are saying. I do find it plausible though that a change of curriculum could have a huge impact. I find some educational practices such as fuzzy math and lack of direct instruction in grammar, spelling, and phonics infuriating:( I have read of too many stories of poor math curricula and others. Plus my ds had schools that encouraged parents to bring in calculators in kindergarten which I find very problematic:001_huh:. This was a at private montessori school and public school.

 

I agree that it is astounding that they are not interested in fielding this at other schools.

[nmoira]

I see what you are saying. I do find it plausible though that a change of curriculum could have a huge impact. I find some educational practices such as fuzzy math and lack of direct instruction in grammar, spelling, and phonics infuriating:( I have read of too many stories of poor math curricula and others. Plus my ds had schools that encouraged parents to bring in calculators in kindergarten which I find very problematic:001_huh:. This was a at private montessori school and public school.

 

I agree that it is astounding that they are not interested in fielding this at other schools.

 

I should clarify by saying that I think the one take-away conclusion would be that the district's current math program is not good for many of the students it serves, and is unlikely to be appropriate for general classroom use.

[Kareni]

And I thought the secret was the Math'n'Stuff store!

 

Regards,

Kareni

[regentrude]

The problem is not the fact that the other math programs are discovery based. You can have excellent rigorous discovery based programs. The problem is that Everyday and Connected Math emphasize conceptual understanding and neglect to teach mastery of actually doing something (fraction strips in 6th grade instead of calculating ratios, "benchmark fractions" instead of knowing how to convert decimal into fraction for any numbers, convoluted "innovative" algorithms instead of traditional quick ones).

Mastery of concept AND algorithm can be accomplished with a discovery approach (AoPS anybody?). Just not with a bad curriculum like the ones mentioned.

[kalanamak]

And I thought the secret was the Math'n'Stuff store!

 

Regards,

Kareni

 

:lol: (I once bought $100 worth of dice there.)

[Spy Car]

I love (don't actually) how people jumped to the wrong conclusions.

 

A "fuzzy" math program is bad, so now all "discovery" math programs are bad? Absurd. We know how valuable great discovery math programs like Miquon and AoPS can be.

 

It reminds me of the Israeli mathematician who blamed Cuisenaire Rods because an Israeli program that incorporated them happened to be a bad program. Where is the logic???

 

Bill

[simka2]

I am just glad to see a school in that area doing better. I really hope they pay attention to what is and is not working.

[nmoira]

I love (don't actually) how people jumped to the wrong conclusions.

 

A "fuzzy" math program is bad, so now all "discovery" math programs are bad? Absurd. We know how valuable great discovery math programs like Miquon and AoPS can be.

 

It reminds me of the Israeli mathematician who blamed Cuisenaire Rods because an Israeli program that incorporated them happened to be a bad program. Where is the logic???

 

Bill

If the blog post had only been a criticism of the district's current programs, I would have linked to the newspaper article instead. :001_smile: We're also talking about middle school students here: Miquon would not be an option, and I don't think AoPS is appropriate for general classroom use.

[Spy Car]

If the blog post had only been a criticism of the district's current programs, I would have linked to the newspaper article instead. :001_smile: We're also talking about middle school students here: Miquon would not be an option, and I don't think AoPS is appropriate for general classroom use.

 

 

It doesn't matter. By attacking all discovery math programs because they happened to choose a bad one (which may or may not actually be a discovery math program) they do collateral damage. And this is so typical in "the Math Wars," where is sometime seems there is only a binary choice between "fuzzy math" and "drill and kill" when (as you know very well) those are not the only options.

 

I don't like having the debate framed only my bad choices. KWIM?

 

Bill

[nmoira]

It doesn't matter. By attacking all discovery math programs because they happened to choose a bad one (which may or may not actually be a discovery math program) they do collateral damage. And this is so typical in "the Math Wars," where is sometime seems there is only a binary choice between "fuzzy math" and "drill and kill" when (as you know very well) those are not the only options.

 

I don't like having the debate framed only my bad choices. KWIM?

 

Bill

Fair enough, though I hope you noticed that Singapore was one of term alternative programs being used. I got a bit of a chuckle out of its being described as a "traditional" program. :D

[NoPlaceLikeHome]

I love (don't actually) how people jumped to the wrong conclusions.

 

A "fuzzy" math program is bad, so now all "discovery" math programs are bad? Absurd. We know how valuable great discovery math programs like Miquon and AoPS can be.

 

It reminds me of the Israeli mathematician who blamed Cuisenaire Rods because an Israeli program that incorporated them happened to be a bad program. Where is the logic???

 

Bill

 

I don't think discovery methods are bad at all and even desirable as long as the basics such as mathematical operations and math facts are mastered. IMO the two are not mutually exclusive. Unfortunately, I suspect the mastering of the basics is being left to the wayside in some cases:(.

[creekland]

All I can say is that in our high school we get the "results" of fuzzy math and it's not pretty. There are very few kids who do well with it. The extremely few kids we have who do well on the SAT (esp SAT Math 2) also tell me they have to do a lot of work outside of school in order to be exposed to all the concepts they need.

 

I'm going to be teaching Alg 1 in 7th and 8th grade during a maternity leave for one of our regular teachers. I shadowed her the last couple of days. The dependency on the calculator was appalling. (I had kids who couldn't tell me what times 2 = 200 and had to figure it out by dividing 200/2 on their calculator.) These are our top math students.

 

One of the main issues I see with it (in an overall sense) is that kids are supposed to figure things out themselves. Many start along the wrong track. It's a known fact that the first impression in anything is the one the brain remembers the best. When the kids start incorrectly, the brain remembers that first impression and many remain confused about simple things for the rest of their high school life. They generally also remember being confused and then can't remember which thought was correct and which wasn't. We have several kids who could be good math kids, but they are now convinced they are horrible at math. Our poor math kids have all but given up totally.

 

Another issue is that many learn to "follow the steps" with no real understanding about what they are doing. They are not making the concept jump at all. Very, very few make the concept jump.

 

Then too, remember that in my average classes (across our high school - I rarely do middle school) we have 7 or 8 groups working at once. The teacher, while wandering, can only be assisting one group while they are doing their group work. The other groups often end up talking about everything and anything - except math. A lot of time is wasted. There are a few conscientious kids who absolutely detest the group tests because they are the only ones who are trying and the others get to leech off of them. The tests tend to be incredibly easy - yet many still get really poor grades because the understanding is just not there.

 

I'm not a Saxon fan at the Alg and up level, but at this point, I wish we could choose anything but what we have.

 

And the only reason I've agreed to teach it (for this long term assignment) is because our personal economy is at an all time low and we need the $$. I will absolutely be doing all I can to convey the actual math and that will likely include making a few unconventional changes within the classes I'll have. I don't know how much I'll be able to get away with. I can't add or subtract any assignments, so I'm rather limited.

 

My own youngest is in public school now (his choice - certainly not my preference) and I have him do real math outside of school - alongside the fuzzy math. He's loved in his groups and easily got As in Geometry. He's not my "mathy" kid at all - he just gets exposure to real math. I made sure he got through Alg 1 at home before getting into the crappy math. That definitely helped him.

 

Our top math teacher (College Alg) told me this year has been her worst for having well-prepared students. Counting back the years, this year's class is the first to have gone through Alg 1 on up with the new books (we use CPM math). Does she make the connection? Of course not. She's the one who sells the books to our school. :glare:

 

Our school will go under state control next year if we don't pass state standards again this year (3rd year in a row). I'm really, really hoping part of their control will be a switch in math programs. I guess I doubt it, but I can hope. Meanwhile, I'm glad that my youngest is a sophomore and after two more years, we'll be done (and I'll likely quit subbing).

[Joyofsixreboot]

I don't think discovery methods are bad at all and even desirable as long as the basics such as mathematical operations and math facts are mastered. IMO the two are not mutually exclusive. Unfortunately, I suspect the mastering of the basics is being left to the wayside in some cases:(.

 

This seems to be the problem in our area. Calculators in first grade and " trust" the spiral isn't working.

[....]

All I can say is that in our high school we get the "results" of fuzzy math and it's not pretty.

 

Our school district uses Everyday Math. I posted about it a year ago. My daughter was helping the neighbor's kid with her math homework. She was trying to multiply two numbers. This kid had numbers everywhere. It took her a looooong time to come up with the answer and she had so many numbers all over the place. In the end, her answer was wrong. Why the heck would you teach math like that? I feel bad for the kids. Also, I'm paying huge property taxes so the school district can teach math like that???

 

Also, like I said before...we use Miquon and intend to continue with AoPS, but our math doesn't look anything like what I saw with Everyday Math. If math could be creepy, EM was creepy.

[....]

Why not?

 

Miquon was originally written for classroom use. Miquon and AoPS would need a special sort of teacher to make it work in a classroom. If you read The First Grade Diary, the dude who wrote Miquon sounded like an unusual teacher.

[stripe]

If you read The First Grade Diary, the dude who wrote Miquon sounded like an unusual teacher.

 

(cough) That dude (Lore) was a lady.

[NoPlaceLikeHome]

That's just so crazy. I'm positive my kids wouldn't have learned how to calculate basic problems had I let them use calculators. They would have loved that though.

 

:iagree:My ds was in a school that wanted us to bring in calculators for kindergarden and first grade and up:glare:

 

When I grew up we did not even have calculators till I was about 14 and even then I don't believe I was allowed to use them until several years into high school.

[creekland]

Our school district uses Everyday Math. I posted about it a year ago. My daughter was helping the neighbor's kid with her math homework. She was trying to multiply two numbers. This kid had numbers everywhere. It took her a looooong time to come up with the answer and she had so many numbers all over the place. In the end, her answer was wrong. Why the heck would you teach math like that? I feel bad for the kids. Also, I'm paying huge property taxes so the school district can teach math like that???

 

Also, like I said before...we use Miquon and intend to continue with AoPS, but our math doesn't look anything like what I saw with Everyday Math. If math could be creepy, EM was creepy.

 

Everyday Math is what our elementary uses. CPM Math is what is used from middle school on up. Both have me so jaded against fuzzy math programs that I would never want to see one in a public school.

 

When homeschooling, I think one ought to pick a curriculum that works for the student - that might be discovery or traditional. In ps, since one needs to educate the masses, traditional is better IMO.

 

I found one comment under the article interesting - this one:

 

Great post, Cliff! On a related note - there are now DEFINITIVE studies that demonstrate a DIRECT correlation between drilling (math, spelling, even cursive handwriting) and REDUCTION of attention deficicit disorder. Go figure! (Literally........ pun intended....)

December 6, 2011 1:09 PM Now I'm curious as to which definitive studies s/he's talking about. Anyone know or with more time to search?

[FaithManor]

Everyday Math is what our elementary uses. CPM Math is what is used from middle school on up. Both have me so jaded against fuzzy math programs that I would never want to see one in a public school.

 

When homeschooling, I think one ought to pick a curriculum that works for the student - that might be discovery or traditional. In ps, since one needs to educate the masses, traditional is better IMO. QUOTE]

 

 

This is what we have in our local elementary too. The children use calculators from 2nd grade forward. According to one elementary teacher that I personally know, this is because, "The children never actually memorize any math facts so we have to make them calculator dependent in order to keep grades high. With budget cuts, the teachers with the fewest honor-roll students get let go. I've got 4th graders that cannot tell me what 3 x 3 is, but they are A students because of that calculator. But, then, this is fuzzy math...I've got a lot of kids that can reasonably guess a right answer, but couldn't actually do the alorhythm to get the right answer. Most of my 4th graders do not know how to carry or borrow/re-group. I've been teaching 20 years and I wish I could retire now. I hate my job!"

 

Sigh...direct quote...or pretty close because we were discussing this after church last Sunday.

 

The same school district considers a 4th grader to be mathematically gifted and pulls them out for 30 minutes once per week for math enrichment because.....are you ready for this......they've actually memorized their multiplication tables through the 4's!!!!! I'm not kidding. They tell these kids they are gifted for having accomplished this. No wonder my other dear friend, one of the primary algebra 2 and trig teachers for the high school, has moments of abject dispair because his students are getting credit for algebra 2 but he's actually teaching mostly algebra 1 and "HOW TO ADD, SUBTRACT, MULTIPLY, AND DIVIDE FRACTIONS". Forget Trig....he's lucky if he gets these kids through a couple of chapters of algebra 2 after all of that remedial work. Of course, he was completely down on the elementary and middle school teachers until I told him to take the time to educate himself on the curriculum they are stuck with, number of students in the classroom, etc. A few weeks later his comment was, "I'd be suicidal if I had to deal with their lot in teaching!"

 

I think that if something happened to me, I'd come back as a ghost and continue homeschooling my children just to keep them out of that system.

 

Faith

[NoPlaceLikeHome]

Everyday Math is what our elementary uses. CPM Math is what is used from middle school on up. Both have me so jaded against fuzzy math programs that I would never want to see one in a public school.

 

When homeschooling, I think one ought to pick a curriculum that works for the student - that might be discovery or traditional. In ps, since one needs to educate the masses, traditional is better IMO.

 

I found one comment under the article interesting - this one:

 

Great post, Cliff! On a related note - there are now DEFINITIVE studies that demonstrate a DIRECT correlation between drilling (math, spelling, even cursive handwriting) and REDUCTION of attention deficicit disorder. Go figure! (Literally........ pun intended....)

December 6, 2011 1:09 PM Now I'm curious as to which definitive studies s/he's talking about. Anyone know or with more time to search?

 

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:

Edited December 7, 2011 by priscilla

[NoPlaceLikeHome]

Everyday Math is what our elementary uses. CPM Math is what is used from middle school on up. Both have me so jaded against fuzzy math programs that I would never want to see one in a public school.

 

When homeschooling, I think one ought to pick a curriculum that works for the student - that might be discovery or traditional. In ps, since one needs to educate the masses, traditional is better IMO. QUOTE]

 

 

This is what we have in our local elementary too. The children use calculators from 2nd grade forward. According to one elementary teacher that I personally know, this is because, "The children never actually memorize any math facts so we have to make them calculator dependent in order to keep grades high. With budget cuts, the teachers with the fewest honor-roll students get let go. I've got 4th graders that cannot tell me what 3 x 3 is, but they are A students because of that calculator. But, then, this is fuzzy math...I've got a lot of kids that can reasonably guess a right answer, but couldn't actually do the alorhythm to get the right answer. Most of my 4th graders do not know how to carry or borrow/re-group. I've been teaching 20 years and I wish I could retire now. I hate my job!"

 

Sigh...direct quote...or pretty close because we were discussing this after church last Sunday.

 

The same school district considers a 4th grader to be mathematically gifted and pulls them out for 30 minutes once per week for math enrichment because.....are you ready for this......they've actually memorized their multiplication tables through the 4's!!!!! I'm not kidding. They tell these kids they are gifted for having accomplished this. No wonder my other dear friend, one of the primary algebra 2 and trig teachers for the high school, has moments of abject dispair because his students are getting credit for algebra 2 but he's actually teaching mostly algebra 1 and "HOW TO ADD, SUBTRACT, MULTIPLY, AND DIVIDE FRACTIONS". Forget Trig....he's lucky if he gets these kids through a couple of chapters of algebra 2 after all of that remedial work. Of course, he was completely down on the elementary and middle school teachers until I told him to take the time to educate himself on the curriculum they are stuck with, number of students in the classroom, etc. A few weeks later his comment was, "I'd be suicidal if I had to deal with their lot in teaching!"

 

I think that if something happened to me, I'd come back as a ghost and continue homeschooling my children just to keep them out of that system.

 

Faith

To me that is very sad if they consider someone gifted for having memorized only some of the math facts:( The thing is I believe most normal kids can easily master and understand all of the math facts and more.

 

These sort of stories make me glad to be doing school at home:) I feel bad for kids subjected to this educational neglect in the some of the schools.

[Spy Car]

There is a world of difference between doing post-mastery drill after a child has a solid understanding of the mathematics involved in given operations and attempting to jump over this stage of instruction by replacing (or largely replacing) solid math instruction with "teaching" via drill.

 

To have a sound math education a child should have a firm grasp of how the math works, be able to articulate the reasoning of operations, be able to invoke the mathematical laws at play in the operations they are learning, be capable of multiple mental math strategies for solving problems, be highly competent in working the standard algorithms (while understanding why they work), and ultimately have fast recall of "math facts."

 

But that other stuff needs to happen before you sit an memorize and drill "math facts" or you just won't be teaching for mathematical understanding.

 

I've said it before, but the other approach is like teaching a child to read by having a stack of words on flash-cards that the children are supposed to memorize by the way they look. It can be done, but it short-cuts the learning process and potentially leaves big holes of understanding that can bite you later.

 

Bill

[NoPlaceLikeHome]

There is a world of difference between doing post-mastery drill after a child has a solid understanding of the mathematics involved in given operations and attempting to jump over this stage of instruction by replacing (or largely replacing) solid math instruction with "teaching" via drill.

 

To have a sound math education a child should have a firm grasp of how the math works, be able to articulate the reasoning of operations, be able to invoke the mathematical laws at play in the operations they are learning, be capable of multiple mental math strategies for solving problems, be highly competent in working the standard algorithms (while understanding why they work), and ultimately have fast recall of "math facts."

 

But that other stuff needs to happen before you sit an memorize and drill "math facts" or you just won't be teaching for mathematical understanding.

 

I've said it before, but the other approach is like teaching a child to read by having a stack of words on flash-cards that the children are supposed to memorize by the way they look. It can be done, but it short-cuts the learning process and potentially leaves big holes of understanding that can bite you later.

 

Bill

I wholeheartedly agree with you. The thing is though I get the impression from what I hear about some schools that mastering the math facts or grammar or spelling or cursive are not necessary even when one has an understanding. My ds was clearly taught an understanding of mathematical operations with manipulatives and pictures and demonstrations via SM and the like:D He has also been given lots of practice and "drill" so to speak in a variety of ways including many fun ones. I suspect some schools are skipping this part or only breezing over it:(. We have also moved on to other math concepts besides the basics while still learning these facts because he had a firm understanding of them and to prevent monotony and break up the practice part.

[nmoira]

Why not?

 

Opt-in advanced classes, yes. I think the material is too challenging to be used at grade level as a core program in a mixed ability classroom.

[....]

(cough) That dude (Lore) was a lady.

 

:lol: Oh. my. goodness. I have no idea why I thought it was a man. Darn its. OK, SHE was an unusual teacher. :D

[Tammyla]

Wow. ;)

 

http://cliffmass.blogspot.com/2011/12/seattles-math-secret-revealed.html

 

I don't think many here will be surprised by the "secret."

[Tammyla]

:iagree:

 

Unfortunately, I'm not surprised. I am ticked off at the superintendent's response, though.

[wapiti]

Opt-in advanced classes, yes. I think the material is too challenging to be used at grade level as a core program in a mixed ability classroom.

 

I think this is right. I actually emailed Richard this basic question a while ago, about using AoPS in a regular classroom, and he said there would have to be a very special teacher. There might be one private school where this is occurring. Still, I'm hoping I can convince my kids' school to use it for the most advanced ability groups. My kids are starting to skew my perception of what is and is not reasonable for the middle of the pack. I still wonder what would happen if these books, perhaps without the challenge sets, were used in a regular classroom at grade level (prealgebra in 8th? though this seems to be moving down to 7th) with kids who actually had a solid elementary math education.

[FaithManor]

There is a world of difference between doing post-mastery drill after a child has a solid understanding of the mathematics involved in given operations and attempting to jump over this stage of instruction by replacing (or largely replacing) solid math instruction with "teaching" via drill.

 

To have a sound math education a child should have a firm grasp of how the math works, be able to articulate the reasoning of operations, be able to invoke the mathematical laws at play in the operations they are learning, be capable of multiple mental math strategies for solving problems, be highly competent in working the standard algorithms (while understanding why they work), and ultimately have fast recall of "math facts."

 

But that other stuff needs to happen before you sit an memorize and drill "math facts" or you just won't be teaching for mathematical understanding.

 

I've said it before, but the other approach is like teaching a child to read by having a stack of words on flash-cards that the children are supposed to memorize by the way they look. It can be done, but it short-cuts the learning process and potentially leaves big holes of understanding that can bite you later.

 

Bill

 

 

Bill, I do agree. It is a balancing act because both worlds of "math" need to be mastered. The problem we have in our area is that there is no drill, there is no taking the time to master any one skill...everyday is a new concept, everyday is calculator dependent with 2ND GRADERS, etc. The teachers tell me that when there is a new concept, the students have maybe ten problems of that and then the teachers are required to give the student standardized test prep worksheets for the remainder of the math instructional time. This is not balance; it's insanity. Young children are not in the logic stage of learning yet, so they need to not only have their hand held through the process of understanding how the algorhythm works, but also getting some memory recall of their math facts as this is the time in their life when they can memorize easily. They need to drill the new idea until they quickly recall the process. I'm all for Singapore Math as long as the extra-practice book is used because I think that is a blending of both necessities. I use Singapore Math at home and I have Rod and Staff around for pulling out extra work when we need some more problems/repetition in order to cement the new concept.

 

Unfortunately, given that the kids in our area are reaching 9th grade without knowing their multiplication tables, nor being able to divide fractions, and this is not limited to a handful of students but more than 50% of the freshman class (by admission of the head of the high school math department), one has to consider that either discovery math itself or the implication of discovery math has been a bad thing in our school district. These kids are literally, math illiterate and with an average district score of 17.5 on the math portion of the ACT, one cannot make the case that they shouldn't be memorizing and drilling some math facts. If one looks at that test, knowing one's math facts plus even a little bit of algebra 1, with all of the test prep this school does, the school should at least have an average of 20 on that section.

 

I do know that I had what one would call "traditional" math in school and my friends and I scored WAY over the national average on the ACT and SAT and I for one, was not a confident math student at that time. I had also not been given ANY test prep to get ready for it either. So, I smell a rat and that rat is "fuzzy math".

 

My dad just had a 19 year old graduate of the local high school come into his shop and ask about a job. The boy was a B student at the high school. We've known him for a while. Nice kid, considered pretty bright, and of course, decent grades. Dad handed him a 2.5" nut and three metric crescent wrenches. He told the young man not to be nervous and to take his time, but if there are approximately 2.5 centimeters per inch, which metric wrench would come closest to a tight fit on that nut. The boy spent ten minutes thinking about it and then told dad he couldn't figure it out??????? It just makes one wonder what on earth goes on in that school district from K-12 that a B average stdent can't figure that out!

 

This school district needs to do something beside the curriculum they have now and I think it either needs to be Singapore with extra drill, or it needs to be something traditional so that whether or not they understand how it works, they can at least do simple calculations and not be completely ignorant.

 

Faith

[kiana]

This school district needs to do something beside the curriculum they have now and I think it either needs to be Singapore with extra drill, or it needs to be something traditional so that whether or not they understand how it works, they can at least do simple calculations and not be completely ignorant.

 

Faith

 

Yes. This.

 

I'm not down on discovery math IN GENERAL. I think that with a teacher who really knows and understands their topic, AND with a group of students who are capable of working on-topic, it would be wonderful and far superior to the traditional programs like Saxon.

 

BUT.

 

Especially in elementary school, many teachers are AFRAID of math. They don't understand enough of it to know if and when the students are going down a mathematically correct track or whether they're completely on the wrong track. They don't know the questions to ask to guide them to a correct answer AND they don't take the time to learn.

 

Furthermore, they're working with groups of disparate students all trying to "discover" ... so unlike a homeschool parent who can sit down and figure what this kid's trying to discover and what the reasoning is, they need to be skilled enough to deliver "drive-by assistance"

 

If a school has teachers like these and can NOT simply replace them or somehow make them learn math, they are probably better off with a traditional drilling program and letting them learn the why later, than letting them grow up ignorant of both the how and the why and knowing only that math is confusing.

[Perry]

To have a sound math education a child should have a firm grasp of how the math works, be able to articulate the reasoning of operations, be able to invoke the mathematical laws at play in the operations they are learning, be capable of multiple mental math strategies for solving problems, be highly competent in working the standard algorithms (while understanding why they work), and ultimately have fast recall of "math facts."

 

 

Bill

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

[butterflymommy]

Unfortunately, I'm not surprised. I am ticked off at the superintendent's response, though.

 

There are millions of dollars at stake in curriculum deals. If she admits Saxon is better than their current fuzzy math program, she's admitting to a huge amount of money down the toilet. I'm pretty sure districts can be locked into contracts with curricula providers, perhaps hers currently is, and she couldn't change if she wanted to.

[TravelingChris]

LIfe of Fred is another discovery math program. It has worked very well for my two younger kids.

 

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.

[wapiti]

Especially in elementary school, many teachers are AFRAID of math. They don't understand enough of it to know if and when the students are going down a mathematically correct track or whether they're completely on the wrong track. They don't know the questions to ask to guide them to a correct answer AND they don't take the time to learn.

 

Furthermore, they're working with groups of disparate students all trying to "discover" ... so unlike a homeschool parent who can sit down and figure what this kid's trying to discover and what the reasoning is, they need to be skilled enough to deliver "drive-by assistance"

 

If a school has teachers like these and can NOT simply replace them or somehow make them learn math, they are probably better off with a traditional drilling program and letting them learn the why later, than letting them grow up ignorant of both the how and the why and knowing only that math is confusing.

 

I am so bitter about this. Most of my kids are in school, and all depends on which teacher they get. If they don't get a teacher I "approve" of, I will pull them out to homeschool. While there is no perfect school, I am feeling bitter and resentful that I can't seem to find a school that is consistently "good enough" in various categories that I deem important, math being #1 (fwiw, I admit my kids are "different," 2e-ish, which has me looking for an even more unusual niche). It has gotten to the point where even if I'm hs-ing one kiddo next year, I might still try to volunteer to teach a math ability grouping at my other kids' charter school, if they'd have me.

[Spy Car]

Bill, I do agree. It is a balancing act because both worlds of "math" need to be mastered. The problem we have in our area is that there is no drill, there is no taking the time to master any one skill...everyday is a new concept, everyday is calculator dependent with 2ND GRADERS, etc.

 

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.

 

 

The teachers tell me that when there is a new concept, the students have maybe ten problems of that and then the teachers are required to give the student standardized test prep worksheets for the remainder of the math instructional time. This is not balance; it's insanity.

 

No argument here.

 

Young children are not in the logic stage of learning yet, so they need to not only have their hand held through the process of understanding how the algorhythm works, but also getting some memory recall of their math facts as this is the time in their life when they can memorize easily. They need to drill the new idea until they quickly recall the process.

 

I think some of the arguments about what children can or can't understand because they are in a "Grammar Stage" or a "Logic Stage" are pretty dubious, to tell you the truth. I know it is heresy on this forum, but there is a way to teach for understanding in ways that are very comprehensible to children. To my mind it is "classical" to teach children the "grammar" of math rather than simply creating parrots. As that not classical education, and there is (to my mind) wide-spread confusion on this point).

 

I'm all for Singapore Math as long as the extra-practice book is used because I think that is a blending of both necessities. I use Singapore Math at home and I have Rod and Staff around for pulling out extra work when we need some more problems/repetition in order to cement the new concept.

 

We use the IPs. But I've said I like the Standards Edition in part because of the additional practice and review. I agree that computational skills should be sharp.

 

Unfortunately, given that the kids in our area are reaching 9th grade without knowing their multiplication tables, nor being able to divide fractions, and this is not limited to a handful of students but more than 50% of the freshman class (by admission of the head of the high school math department), one has to consider that either discovery math itself or the implication of discovery math has been a bad thing in our school district.

 

It is a deplorable situation. I just don't think one can say because "fuzzy math" programs like Everyday Math, TERC, or Connected are lousy math programs (and ones I'm not convinced qualify as "discovery math" programs) that we should take the leap to the proposition that all discovery math is bad. Because that is an illogical leap. It lumps in some of the most interesting and efficacious math programs with some of the worst, and also lumps programs which have little (or nothing) in common.

 

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.

 

These kids are literally, math illiterate and with an average district score of 17.5 on the math portion of the ACT, one cannot make the case that they shouldn't be memorizing and drilling some math facts.

 

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.

 

I do know that I had what one would call "traditional" math in school and my friends and I scored WAY over the national average on the ACT and SAT and I for one, was not a confident math student at that time. I had also not been given ANY test prep to get ready for it either. So, I smell a rat and that rat is "fuzzy math".

 

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.

 

My dad just had a 19 year old graduate of the local high school come into his shop and ask about a job. The boy was a B student at the high school. We've known him for a while. Nice kid, considered pretty bright, and of course, decent grades. Dad handed him a 2.5" nut and three metric crescent wrenches. He told the young man not to be nervous and to take his time, but if there are approximately 2.5 centimeters per inch, which metric wrench would come closest to a tight fit on that nut. The boy spent ten minutes thinking about it and then told dad he couldn't figure it out??????? It just makes one wonder what on earth goes on in that school district from K-12 that a B average stdent can't figure that out!

 

This school district needs to do something beside the curriculum they have now and I think it either needs to be Singapore with extra drill, or it needs to be something traditional so that whether or not they understand how it works, they can at least do simple calculations and not be completely ignorant.

 

Faith

 

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

[creekland]

 

 

No wonder my other dear friend, one of the primary algebra 2 and trig teachers for the high school, has moments of abject dispair because his students are getting credit for algebra 2 but he's actually teaching mostly algebra 1 and "HOW TO ADD, SUBTRACT, MULTIPLY, AND DIVIDE FRACTIONS". Forget Trig....he's lucky if he gets these kids through a couple of chapters of algebra 2 after all of that remedial work. Of course, he was completely down on the elementary and middle school teachers until I told him to take the time to educate himself on the curriculum they are stuck with, number of students in the classroom, etc. A few weeks later his comment was, "I'd be suicidal if I had to deal with their lot in teaching!"

 

Faith

 

And when I was in for our College Alg teacher last month for roughly 3 weeks, part of what I was teaching was polynomial division. I had to start with simple division, say, 35/6 as most of the kids had no clue how to do it without their calculators. These are our top math students.

 

And in my pre-Calc class last Friday, not a single student knew how to divide 1/(1/10) without their calculator. They couldn't figure out where 1/4 and 1/2 should be respective of each other on a graph either.

 

It's so frustrating that I'm at the point where I want to either change school districts or quit. Financially, we're not at that point right now.

 

Drill and kill is wrong if the student knows what they are doing. It makes math boring. However, when students don't know what they are doing it can help show that and get it fixed.

 

With our fuzzy math kids can muddle their way through and/or leech off their group partners and learn absolutely nothing. They might have all the correct steps down on their paper, but if you ask them what it means, they haven't a clue far more often than not.

 

But according to our school, it's not the fuzzy math that's at issue, it's the school and national tests that don't show our students' ability correctly. :glare:

 

FWIW, my two oldest scored in the 97 and 99th percentiles on their ACT math. I pulled them when we started fuzzy math in the high school. My middle son had had a couple of years of fuzzy math in the elementary school. The first thing I found out is he didn't have a clue about fractions by 7th grade - unless he could use his calculator. It took him 2 days max to get the idea down. Why wasn't he taught in school? It's not like he couldn't handle it. He had peers of his academic ability who stayed in our ps. All but one did considerably worse on their SAT math and that one did a lot outside of school to make up for fuzzy math. So, my guy is getting merit aid offers and they are hoping to make it into good schools knowing they'll need need-based aid or full pay.

 

It kind of makes me angry knowing they are essentially equal in ability IF our school had prepared them well.

 

I'm adamant that my youngest do a real math outside of school. He's not as talented in math (but not horrid) and I don't need him sinking to their level. I'm still aiming him toward merit aid.

Edited December 7, 2011 by creekland