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Phil Daro - Against Answer Getting

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Phil Daro goes into detail on the problems of "Answer-getting," one of the practices that the new Common Core Standards intend to greatly reduce.

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people that they asked me if there was one thing that we could change that would make the biggest difference what would it be it wouldn't be a magic pill it's not going to be easy but it's going to be like a lot of good things that we have to do in life it means changing a bad habit when I look at hundreds of hours of videos of Japanese classrooms where they get high performance from ordinary teachers and hundreds of hours of us classrooms where we get ordinary performance from very good teachers I see the goal of the Japanese teacher is different than the goal of an American teacher the American teacher looks that a problem going to use my lesson and ask themselves how can I teach my kids to get the answer to this problem the Japanese teacher asks what's the mathematics they're supposed to learn I'm working on this problem how can I get them to learn that mathematics now those might not seem so different when you first think about it but they are and we'll see some examples this is what was that the center of my thinking and all the standards work that I did and it fortunately became contagious and this will help you understand why the stand are the way they are going to take a little detour to answer this question in the California tradition is multiple choice so you know obviously number for ZN that's supposed to be correct I watched hundreds of hours of videos of Jack Japanese teachers American teachers German teachers teaching 8th grade in algebra Detroit middle schools not a high schools and one of those it took years for me to finally see the obvious it's one of those American classrooms even our best teachers goal is to teach the kids how to get the answer to today's problem and that goal is the same if your traditional teacher or if your Progressive teacher it's about getting the answer and the Japanese classroom whether you're a good teacher or bad teacher named the same distribution of teachers as we do every kind of people really pedagogique geniuses dollar teaching just like we do I mean it's not a big difference in the pedagogy from the point of view of the teachers capabilities their goal is different American teacher how am I going to teach a speech my kids how to get the answer to this problem the Japanese teacher asked what's the math is supposed to learn from working on this problem how am I going to use this problem to teach that math answers don't just so you don't quote me wrong answers are essential correct answers are essential this is not a talk against the answers but they're part of the process they're not the product the product is the math the kids walk away with in their heads and and their ability to do stuff long answers are part of the process to time and again in the Japanese classroom you'll see gender covered an approach that doesn't work Jen explain your Discovery to the class Jen explains the discovery to the class does everyone understand Jen's Discovery now let's all figure out why I didn't work Jen did you figure out why it didn't work let's figure it out when you do it's actually often easier to get to the math figuring out why an approach didn't work then wide approach did work which is another reason they do this we had a Japanese educator that we are working with not for the standards this was an early a project who criticized us for treating every for treating this situation as Jen's problem something wrong with Jen need to diagnose and remediate that's not the first reaction in a Japanese classroom first reaction is Jen is the canary in the mine shaft that approach that Jen discovered anyway have you might go down that path tomorrow or next week or the week after and he was like this he got the answer real quick chance they might be lucky assumptions he learned last year whatever it is but his understanding is not very robust next week I'll give him a different problem I'll make those same assumptions they won't work for that problem he'll be confused and he'll wind up where Jenna's so I'm treating Jen as a symptom of the whole class not as an individual's psychological problem and so for Parker what I'm doing is making his understanding more robust and deeper so they there is free necessary things we need to do with a math problem answer getting I'm not we're not saying that's bad and then the surf work as what gen was involved in the early days in the surfboard one things we've discovered in trying to figure out why kids have problems with word problems is that they don't even bother to try to make sense of the problem they rushed to answer getting immediately start on your experimental arithmetic with the numbers and they do the easiest I think the strategy is really something that works pretty good in elementary school you look at the numbers and you do the easiest arithmetic you can do with those numbers and if it comes out even stop if it doesn't come out even the next easiest arithmetic keep doing it until it comes out even then stop that'll get you proficient on the CST in elementary school but it's trains them not to make sense of the problems so we've devised technique show you some for delaying answer getting here's what happens on the teacher are you all over the place and terms your preparedness I have to keep going I got a pacing plan I got to finish the book whatever it is not even half of you are prepared for today's lesson so I got a problem that you got to get the answer right to if I think my job is teaching how to do get the right answer there's a lot of different ways to teach you how to get the right answer 7 ways to get the right answer one of those ways is for me to teach you some math you don't know already and then show you how to use that math that you're still not sure you know you're not too sure of you've never used it before you're an absolute rookie using this method beginner to show you how to use that Matthew just learned and you just forgot just remembered again to get the right answer some of you will pick it up right away some of you will struggle get a little wrong this sounds like a classroom management mess I'm not going that way another way I could do it is to show you how to get the right answer with math you already know that's more reliable and a few memory a that sounds better I can keep the class together better you can be stupid usung right answers before the bell rings and since you already know the math will be more reliable it's incredible when you anime star text books and it's even worse when you look in the classrooms with a high percentage of what we teach kids is not mathematics but answer getting techniques so it's a curriculum problem the reason mile wide inch deep we tried we were teaching more topics than anyone else we spend less time for topic than anyone else I'll come back to that okay kids are habituated to answer getting to quote my own daughter when she was in high school Daddy I don't have time to understand it I just want to get it right on the test and she when else with that's what she said as she was folding are both taking her paper and leaving to go call one of her girlfriends a month later she said proudly I know how to get a B in a math class without learning anything when she did the rest of her career she went on to college to be successful and has two wonderful kids my grandkids so here's that question the difference how much can I teach my kids to get the right answer how can I use this problem to teach the math is supposed to learn from it so let's just look at some examples now we've also and adding fractions with unlike denominators we all have methods this is a common method you may not recognize the name but you'll recognize the method which like this you draw the wings and then you draw the body you draw a plus sign for the antenna to remind you a multiplication sign for the tail then you multiply on the winds for x one is for you write it down 3 times 3 is 9 you write it down 9 + I remember for is 13 down here I remember to multiply 4 times 3 is twelve you right in the tail answer 13/12 correct works every time what the does this have to do with algebra this is what how your kid the kids you're getting an algebra got past the fractions test when they were in sixth grade or fifth grade but when you get them they don't know fractions how did they pass the the test they pass the test doing it like this so this is not mathematics this is answer getting this is clutter in the curriculum this takes three or four days to teach get some pass this year's tester this month's test waste time petition the mathematical the mathematics they're supposed to learn when they're adding fractions with unlike denominator would take longer and would be harder for them but you'd be teaching them algebra this is Tim's this is the easiest fraction item on Tim's the easiest fraction on him with unlike denominators if you were a butterfly method you'd be lost so this is this problem in most of the conditions if I put this up here cuz this is a good distinguisher if it's an answer getting a tradition like this this problem is a good detector so you in a lot of countries eighty 90% of the kids got this right in some countries like ours it was down around 20 it was one of those toggle items here's one that's within our range we teach in the books to the whole chapter on setting up a proportion and cross multiplying everyone loves it because the problems are hard the kids can all learn this to get those problems right but what there's these are like 6th graders they're just learning when an equation is why would we show them the equal sign and why would we just as this uneasy understanding of equation show them and call it something else why are we calling it up before and in the same year were saying distance equals rate times time is it for for Chanel relationship wait a minute proportion isn't that A over B equals c over d what is that got to do with distance equals rate times time the word proportional is being used in a different way when you do distance equals rate times time and say it's a proportional relationship you're using the language that will will be used when you get to calculus it'll be used in Algebra 1 and Algebra 2 and geometry proportional if they understand it will serve them well setting up a proportion cross multiplying shows up again in chemistry and then basically it's just an answer getting message why not take a little extra time and say set up an equation and solve an inch who's at one of those for Fortune problems there are nine simple equations that one could set up for every one of those problems and only some of them look like quote proportion unquote there all the cords are equivalent there proportional relationships what what we want is for the kids to see and understand that those nine equations are equivalent and all give the same answer not that there's one of those nine that's imagine and that's teaching how to set it up set up an equation and solve cuz how are they going to solve it there's going to solve it by multiplying both sides by the same thing or dividing both sides by the same thing another words algebra your teaching algebra foil method this is an arc this is algebra first outer inner last everyone doesn't not you it's fast doing reliable than teaching that this is an application of the distributive property to apply the distributive property you have to do it once and then you have to do it twice and the second time you have to do it you have to do it two times two terms the foil method works all chapter long next chapter you have to multiply a binomial times a trinomial what happens to the foil method trivia property still works the way distributive property works with polynomials it's it's very deep and it turns out to be where integration comes from when I get to calculus it's all over the place it's as the foundation canceling so we all tell him kids you know nothing wrong with the word cancel casual now--is cancel this one the  cancels that's when they're three left so the answer is X cubed that's correct what are the Raiders have this this one this this one are there all cancel out answer 0 about half the kids take zero on a standardized test for this sound past will have something like this why are they saying zero it's just a procedure they understand the meeting they should look at this announce anything times as it's in is one you don't have to do anything to stay the same on the top and the bottom it's one so what's canceling really about I'm not against using this word but they should understand what it is X over x equals 1 element for multiplication the reason I went through all of this is another mile wide and Steve we all here that we think someone's doing it to us but one of the things we need to do is think I'm doing it all of us are doing pictures are doing it principles are doing districts are doing it textbooks are doing a test to doing it standards are doing it but this is how teachers do it all these things canceling isn't math so you edit it to the curriculum Matthew just added something to the curriculum most of the time you're not only adding but you're leaving out the Math teachers make teachers have their part in making things mile wide and stiff and mainly it comes in the form of methods for answer getting that avoid the math

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Phil Daro - Against Answer Getting

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