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Tuesday, October 21, 2008
A constructivist approach to ratios and proportion
This is a video that purports to show how questioning can be used in teaching. In it, a teacher has a series of one-on-one conversations with a boy who is working on a math problem. I recognized the problem as coming from Connected Math. There are four recipes for an orange drink, with various ratios of orange concentrate to water. The problem is to find out, for each of the four recipes, how many cups of orange concentrate and water are required to make enough drink for 240 campers. Each camper is to have 1/2 cup.
Typical of CMP, the student in the video has received minimal instruction on ratios and proportions. What's more, the problem is a multi-step one, that requires one to figure out the total amount of cups needed of orange drink, given that of 240 campers, each receives 1/2 a cup. This is not in itself hard, but given that he has minimal instruction, it is all one big jumbled mess of a problem in his mind. He has four such recipes and therefore four problems to do, but as is evident from the first dialogue, he has mushed all four recipes into one.
This problem is not difficult to teach with a systematic direct approach. Singapore Math approaches it using bar s. As an example, if the recipe is 2 parts orange concentrate to 3 parts water, the 2:3 ratio is illustrated as follows:
[ ][ ] Orange drink
[ ][ ][ ] Water
There are a total of five parts that make up the orange drink. If there are 120 cups needed (1/2 cup for 240 campers = 1/2 x 240, which Singapore Math students have learned how to do in 4th grade), then each part is 120/5 = 24 cups, and then it is easy to see that the amount of orange drink is two parts, or 2 x 24 = 48 cups, and water = 3 x 24 = 72 cups.
It doesn't take a long time to teach this, and based on my experience with my daughter, the Singapore approach is quite effective and leads to extensions of the concept whereby students can set up ratos between amount of orange concentrate and total amount of orange drink.
When you view the video it is apparent that it is taking this boy quite a while, through quite a few one-on-one dialogues with the teacher. Personally, I don't know of many classrooms where a teacher is going to have that kind of time to have a one-on-one like that.
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This is Morgan County Middle School in Madison Georgia. Now do you know why I buy Saxon and Singapore off ebay? I guarantee you that every other group in the classroom has one responsible kid doing all the work, while the others chat about football, boys, etc. The teachers are very much into "differentiated instruction" at MCMS and every science class is divided with enough gifted kids to head each small group. It is frustrating and ridiculous. Morgan County is listed in the front of the Connected Math book as a pilot school, so our kids have been brainwashed with this junk for several years (and Everyday Math prior to Middle School). Morgan County High School had the lowest SAT's in 10 years, last year. Wonder why? And guess which State has the 49th lowest SAT's in the country. Morgan County has lower SAT's than the State of Georgia. I am the "only parent who has complained." We have a very high poverty rate in this county, but any child from a low-income home who is naturally proficient in math will never know it, as they struggle to stay awake with this excuse for "math." Keep in mind that college can be FREE in Georgia with the Hope Scholarship. You have to graduate from HS with a 3.0 and keep a 3.0 in college. Georgia Tech is a state school, but our High School has not sent a student to Georgia Tech in three years. 9 (out of +/-220)were accepted to the University of Georgia, last year. There are no other schools in the county. The closest private school is 30 miles, away, as are any other public schools (in neighboring counties). The counties to the east and south of us actually have several students who pay tuition to attend Morgan County schools -can you imagine? The local administrators will not discuss math with me, anymore. The parents in north Atlanta - most of whom went to college- were able to demand a traditional math class for North Fulton schools and Gwinnett County schools. The parents in rural Georgia are too busy trying to put food on the table to worry about the lack of education in our local school system. (And one stay-at-home mom with an engineering degree complaining to anyone who will listen for 7 straight years cannot accomplish anything when the school has it's name in the front of a textbook.)
I am more and more convinced that constructivist math has a liberal elitist agenda, as I watch the poorest among us fall further behind at the expense of the latest fad among PhD's. If one of the PhD's in the UGA Math Ed. dept could actually sit down with a child who is struggling in math, they would realize the idiocy of not mastering basic math skills, while wasting precious class time "discovering" the answer, instead. But would an elitist ever actually sit among the "least of these" if it is not for a photo op? Please pardon the bias.
-from a frustrated Mom in Georgia
You are so wise to get Saxon and Singapore. I just afterschooled my one son for a couple of years (he's LD/ADHD) and I was amazed at how far he progressed.
At the old KTM site we talked a lot about "parallel" teaching--teaching your own curriculum while the school just does whatever. Many of us have found that it can absolutely make a difference.
It does seem that different states get bit by the bug for a while and then start to quietly throw off the offending curriculum. Like you said, though, sometimes they just pick an even worse one. And then sometimes you can't wait for them to figure it out and you have to take action.
Hang in there.
SusanS
Thank you for telling me the name of the school. U of GA got a rather large grant from NSF as part of a Math Sci Partnership. UGA gets money for the ed school people to provide help implementing the NSF-funded atrocities such as EM and CMP. I'm sure Madison benefitted from this largess. The students, however, did not.
I feel sorry for the little boy in the video. He's clearly bright but being led in a ridiculous goose chase when he could get so much further.
Barry - One of the Ed School UGA profs spoke at the Middle School just before the State of GA. implemented its new HS Math program. He helped write the new HS standards for the State and did not know math. He made up his own long-winded problem, which was it's own goose chase, and was so very proud that the problem could not be solved without a calculator. They just don't 'get' math, yet they cannot be convinced of that. One of the lead "math" teachers made up her own problems for Field Day Quiz Bowl - like "If Ed makes $9 selling donuts, but owes his brother $15, how much money does Ed have after he pays his brother?" The kids answered $0. She said the answer was
-$6.
Frustrated Mom in Ga.
That video makes me sick. Do these people call this good teaching? Did you notice the girl that stood there waiting and waiting to ask the teacher a question?
They should put a microphone on the other kids who don't have a teacher to ask PROBING QUESTIONS. I'll bet they weren't talking about math.
Steve, you are clearly defining math too narrowly. In the real world, math is embedded in so many of our everyday activities. Of course those children were talking about math! Football is a math game. And everyone knows boys are good at math, so a conversation about boys is really just a conversation about math.
Don't you see?
Both of my daughters watched this (They both attended this school). One daughter said "This is when I do my homework so that I don't have to bring it home." The other said, "there is not another person in that room talking about math."
-Frustrated Mom in Ga.
One piece of evidence of how well this school's math program is working is that the boy does not know that 3/6 is 1/2. If that does not immediately come to mind for a child in middle school then the student must be seriously behind grade-level expectations in arithmetic -- and if you don't understand simple facts about fractions, proportions are beyond your reach.
The main reaction I had was how insincerely the teacher larder psuedo-praise. I myself was never sure what the problem was, but I could follow along enough to tell that the student was very unsure himself what was expected of him. When he asks, "This isn't the answer?" he means "I'm not sure what the question is." The teacher kept telling him "I really like that ratio" and "you have some really good ideas" and "you're on a roll" etc (all quotes approximate). Kids can recognize the false praise they are getting and compare that to their lack of confidence in what they are doing and conclude that the teacher is giving them some hidden message. Then they have to worry half-unconsciously about interpreting the teacher's hidden meaning and the accursed, half-understood problem.
"...so a conversation about boys is really just a conversation about math."
I stand corrected, but they better be asking probing questions.
"... and conclude that the teacher is giving them some hidden message."
That math is some sort of Zen process that requires the development of "thinking". At least Professor Harold Hill knew he was a fraud when he pushed his "think method" in The Music Man.
"This is a video that purports to show how questioning can be used in teaching."
College-trained teachers need to be taught how to ask leading questions? But are they suggesting that this should be done by teachers or students? If this is the teacher's job, then how effective is the process with a one-on-one approach? She could design a directly-taught lesson where she would ask leading questions for the whole class. She would have much better control of the process and could ensure that more light bulbs go off. Imagine. Discovery works better under teacher control.
Even if you believe in this sort of thing, the video is very poorly done. All you know at the end is that the boy is on a roll and should be buttered up. I didn't see any light bulbs go on. It's not clear that he will ever get the problem done correctly. If he does manage to stumble on the answer, I'm sure he will not feel better prepared to tackle the next.
It would be more important to see how the teacher wrapped up the process and made sure that learning did take place. I'll bet they spent the entire class period on this one problem.
This is when I do my homework so that I don't have to bring it home
How did I miss this video???
I'm not reading my own blog!!!
(No time now, unfortunately.)
What I love about all this (that's "love" in quotation marks) is that no one is listening to the kids.
"This is when I do my homework so that I don't have to bring it home" --- why is this child's observation not considered "data"?
That's a rhetorical question.
Even if you believe in this sort of thing, the video is very poorly done. All you know at the end is that the boy is on a roll and should be buttered up. I didn't see any light bulbs go on. It's not clear that he will ever get the problem done correctly.
The problem is, there are people who will view this video and think it's wonderful, and think that the kid is getting "deep understanding". The direct approach that Singapore uses is viewed by such people as "superfluous" and "rote memorization".
I'm getting to the stage now that even though I know what I believe, I begin to feel guilty for advocating direct instruction, much as someone who's been called names (such as "maggot" or other derogatory things) begins to believe that what people are saying about him/her are true. These edu-zealots are wrong. And in my opinion NO RESEARCH IS NEEDED TO PROVE IT, anymore than you need a research study to prove that jumping out of an airplane without a parachute results in death.
Unfortunately you can't ask the zealots how they learned math and hope to get anywhere because they will tell you they were lost in math and didn't get it. Then they will blame the traditional method for their failure.
"Even if you believe in this sort of thing, the video is very poorly done. All you know at the end is that the boy is on a roll and should be buttered up. I didn't see any light bulbs go on. It's not clear that he will ever get the problem done correctly."
That's right. I watched the whole thing, and I didn't see the lights going on--I just saw one worried and confused kid being "helped" at great length, and a bunch of others doing heaven knows what.
--I just saw one worried and confused kid being "helped" at great length, and a bunch of others doing heaven knows what.
And that kid will always think he is "bad at math," simply because he doesn't enjoy the silly way it has been obscured by too many words. Many kids love to actually complete a page of problems, but the educrats cannot imagine that.
Unfortunately you can't ask the zealots how they learned math and hope to get anywhere because they will tell you they were lost in math and didn't get it. Then they will blame the traditional method for their failure.
Exactly - very few teachers or administrators enjoyed math as students. They never caught on and cannot imagine that some people are naturally good at math (real math). A gifted teacher of my daughter's once said "I never liked math, anyway" - this was after I asked if she could send home some math homework for my 3rd grader because the six once-a-week math boxes in Everyday Math were not helping her master anything as it "spiraled" so often. (She couldn't send home any more problems because it would "eat into" her "copy budget." Thankfully, the principal was not amused with her answer and agreed to start requiring that the 4th graders memorize their multiplication facts (shhh- don't tell the Everyday Math textbook salesmen or their pushers (educrats)).
-Frustrated Mom in Ga.
"And in my opinion NO RESEARCH IS NEEDED TO PROVE IT, anymore than you need a research study to prove that jumping out of an airplane without a parachute results in death."
Of course. In the video, the kids could be sitting in rows answering the teacher's probing questions; direct instruction discovery. Forget the fact that her technique is poor, she is helping only one child at a time. It could be that some kids learn better if they are left alone, but that's a poor commentary on teaching standards.
Sometimes I feel that I have to take their side just to get a good argument. We don't see the whole lesson plan, so let's assume that the teacher gets the kids back together afterwards to focus on the target skill and understanding. Let's also asusme that the group discovery phase takes only half the class time. Will the teacher then resort to direct instruction? If not, then how does she get everyone on the same page? What about the kids who are still confused and now frustrated. Will they have the patience to go through the problem one more time?
I have had classes where the teacher poses a problem and then lets the students work on it for a while. Smart teachers won't do this very often and won't let the kids waste too much time. Creating a problem and scaffolding that causes the light bulb go off is very difficult, and it will happen for only a few kids some of the time. What do you do with the rest? You have to teach them! It's quite ridiculus to think you can build a teaching methodology around discovery or projects, especially one that centers on group class work. The giveaway is that they want everything to happen in class and in a group, as if discovery can't happen with direct teaching or with individual homework.
Oh my, that was painful to watch! Unfortunately, I see nearly the degree of confusion at the post-secondary level as well. Anything multi-step or involving substitutions/generalizations is guaranteed to give conniption fits.
why is this child's observation not considered "data"?.
Ask a gifted kid what he or she thinks about "group work" -like in the above post, Children don't like group learning.
They hate it.
They really hate group grades.
-Frustrated Mom
"...and agreed to start requiring that the 4th graders memorize their multiplication facts ..."
Most smart schools trade coverage for mastery. Unfortunately, it makes EM look better than it really is. Salesmen don't care about anything but their commission, and even EM doesn't care, as long as you don't switch to another curriculum. Wink, wink, nudge, nudge.
Frustrated Mom - It will be getting worse in Georgia. NSF Grant #0831774 (Week of 9/21/08)is for PRISM Phase II to extend and "replicate" the changes in math and science instruction in K-12 in Ga of the type shown in video. The MSP partnership is with the University System of Georgia which plans to implement these math and science "reforms" at all 35 public colleges and universities in Georgia.
GA clearly needs some parent websites informing the public about all of this and what it means. There are many that have cropped up in various states over the years.
Illinois Loop (website is on the sidebar to the left) has a list of some of them.
SusanS
GA clearly needs some parent websites informing the public about all of this and what it means. There are many that have cropped up in various states over the years.
One group in north Atlanta had an active group protesting the new HS integrated math, for a while, and attained traditional math options for their district, only. Now they appear to be innactive.
I've been reading the Washington and Illinois websites for a few years. (Plus this blog and Joanne Jacobs). I forward articles to my school board reps and Assistant Supers and principals, on occasion. It doesn't help that the State Super thinks "reform math" is the next great thing, and the UGA Math Ed dept keeps getting awards. Not to mention the whole "name in the front of the Connect Math book" challenge I face at the local level.
I wish the Georgia Tech profs would speak out against "reform math."
Have you heard about the new statewide HS curriculum, where the kids don't have Algebra, Geom, etc, anymore, just Math 1, Math 2, etc? It's integrated - they get a little of each math concept spread out over 4 years. No one with a math-mind has a voice at the State Board of Ed.
-Frustrated Mom in Ga.
It will be getting worse in Georgia. NSF Grant #0831774 (Week of 9/21/08)is for PRISM Phase II to extend and "replicate" the changes in math and science instruction in K-12 in Ga of the type shown in video.
Just peachy.
Barry Garelick mentioned a grant above. It was for $34.6 million and the State Board of Ed was one of the grantees. It ended on Sept 30, 2008 and now we have Phase II.
Phase I was why we have an integrated math requirement in high school. I assume Phase II will smooth the transition to college.
On October 11, 2006 the Board of Regents adopted a "reward" incentive for all USG (also a grantee) faculty that reads like a gag rule against criticizing these math and science reforms. I believe that's the reason for the quiet about what has been done to the high schools. You can be an advocate or salary, tenure. promotion, etc. are at issue.
My town in CT introduced IMP (Integrated Math Program) a couple years ago for the general math track. They also taught algebraI, II, and geometry in a more advanced track.
Thanks to the wonders of disaggregated data, it was clear that kids in IMP failed to make goal on the state 10th grade test, but kids in the traditional math sequence succeeded. Now we are quietly phasing out IMP. Very quietly.
Nobody is going to go on record that IMP was a disaster. It will be gone and life will go on as if it never happened (except for those unfortunate kids that didn't pass the state test because of their lousy math curriculum).
But without NCLB, we'd have never gotten the kind of disaggregated data that makes these kinds of side by side comparisons possible.
"I assume Phase II will smooth the transition to college."
You have to watch out for people who talk about K-16 education. Since some colleges are state supported, they are subject to pressure from the state's K-12 educational community. It seems that integrated and project-based learning is infiltrating colleges.
If you lower expectations for K-12, then state supported colleges have to do the same. Does anyone have any data on how many remedial college classes are now getting full college credit?
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