Tuesday, November 16, 2010
The Einstein Academy charter school in South Park was shocked to discover that its elementary and middle school students, who were sailing along in math, couldn't handle algebra. So the school found a new approach, which so far has proved successful.
The Einstein Academy charter school in South Park was shocked to discover that its elementary and middle school students, who were sailing along in math, couldn't handle algebra in later grades. So the school found a new approach, which emphasizes thinking and reasoning, rather than performing columns of tasks.
Guests: Emily Alpert, education reporter, Voiceofsandiego.org
David Sciarretta, Middle School Principal, Albert Einstein Academy
E. Paul Goldenberg, Distinguished Scholar of Teaching and Learning, Education Development Center
MAUREEN CAVANAUGH: I'm Maureen Cavanaugh. You are listening to These Days on KPBS. Lots of students sail on through arithmetic adding dividing and multiplying, even fractions, numbers are our friends in the early grades and test grades usually run pretty high but then instead of just numbers but there are letters too and we are supposed to figure out what numbers the letters stand for. It is the dreaded algebra, the foundation of higher mathematics, but too often the downfall of the students love affair with math. Lately the Einstein a Academy, a San Diego charter school, has been tackling the algebra question head-on with a whole new approach to teaching math. I'd like to introduce my guest Emily Alpert is the education reporter for the voice of San Diego.org. Emily welcome thank you and principal David Sciarretta is Principle of the middle school and the Alpert Einstein Academy and David welcome, thank you Marty. And Dr. Paul Goldenberg is distinguished scholar of teaching and learning at the educational development Corporation, Dr. Goldenberg, good morning. Good morning, Morgan picks for having me. You are very welcome thank you for joining us this morning. Emily recently filed a report about how the Einstein school solved its math problem. First of all tell us a little bit about math performance in schools before and after algebra.
EMILY ALPERT: Well it's pretty striking in early elementary grades you will see pretty solid math performance for instance in San Diego unified about 70% of students are doing well in math around fourth grade. And then through the middle years of drops and especially precipitously around the time when algebra is talk around eighth and ninth grade. So for instance in San Diego unified UC district where there is fourth grade math scores around 70%. Go down to about 17% in 11th grade. And that's pretty typical of schools around the country. It's not unique. You'll find that students who seem to be doing very well in math up until that point will suddenly really really struggle with algebra.
MAUREEN CAVANAUGH: I wanted to invite our listeners to also join the conversation because I know those children are not alone. Has your child struggled with higher forms of math. You think there's a better way of teaching math in schools. You can give us a call with your questions and your comments and personal stories if you'd like to share them at 1-888955727. That's 1-888895 KPBS. Your story focuses on the Einstein Academy in South Park. Tell us a little bit about this charter school.
EMILY ALPERT: One of the reasons I thought it was especially interesting to look at what Einstein had done is Einstein is a pretty high performing school. It's a school where in the elementary grades math scores are pretty darn high and it's a place that a lot of people are trying to get their kids into. So the fact that a very desirable school would also be struggling with the same issues I think shows how widespread they are. And if it can probably talk a little bit more about the specifics but what they were seeing is you know, kids who had always done very very well would get to algebra and at one point about three years ago I think it was about 9% of students were proficient on State algebra tests which was pretty striking when you look at just how well they were doing before. And so I think the simple answer would've been for the school to kind of jump on the eighth grade math teacher and say what the heck is going on here and thankfully they didn't do that. They took a broader look at said what is it that kids aren't getting before eighth grade that is not equipping them to understand algebra properly.
MAUREEN CAVANAUGH: Principal Sciarretta, what was was at the eighth grade school math teacher, or what was the problem?
DAVID SCIARRETTA: We just one clarification too, here, is that we are actually two charter schools on the same campus. We have many values and mission in common that we are divided into 68, two different schools so the effort really represents collaboration between our elementary school and principal Vaughn and her teachers at myself and my middle school teachers. And the easy answer would've been to point till fingers at an eighth grade algebra teacher and that would be it. Though we realized in Jeanette Vaughn and I have had many conversations about the fact that when we went into many questions in middle school and also elementary school students could compute and the algorithms were accessible to them it was a comfort zone. But when they were asked to deviate from that they were lost so a simple estimation, they were completely at sea when it came to that. And so neither Jeanette nor I are math experts, but we thought there was something to this end we are both international baccalaureate schools that were based on inquiry and reflection so we really approached it from that perspective and begin to look at what was happening in elementary, per elementary we are talking about grades were 80 and 90% were proficient and advanced it would've been easy to say if it ain't broke, don't fix it, but we realized there was something deeper there. So we retained a math consultant,-Aldo came in and did some work with us in Jeanette and I did some work with our teachers and I have to say that efforts, none of this would've been possible if our teachers really didn't buy into taking a deeper look at what they are doing and in elementary school gym and had a cohort of math teachers who exploit this and did not middle school I have two math teachers that we are very small and they were all on board and they wrestled with this and they were courageous even having reporter come to the classroom and the photographer. You don't see that a lot in education and I didn't impose that. Emily can tell you look at the teachers are open to you, and you can go in, if not it's not going to happen.
MAUREEN CAVANAUGH: Dr. Paul Goldenberg as somebody who studies the way people learn and away subjects are taught especially the way math is taught, when kids camps, were scoring good very well on tests and yet they can't make simple estimations when it comes to mathematical problems what does that tell you.
DR. DAVID GOLDENBERG:One of the thoughts that I was having, that, when children learn to compute using the the algorithms, the algorithms are a real favor to get into the computation but they hide some of the thinking and in fact that's actually the purpose with the algorithms, shouldn't say when the algorithms were developed as if there were a single time, but the standard ways of doing things were necessitated by people having jobs in which they had to do a lot of computations.
MAUREEN CAVANAUGH: Excuse me, but tell us what an algorithm is. Give us an example.
DR. DAVID GOLDENBERG:Oh, it's a method for doing a problem without having to think much about it. So for example you are multiplying 22 digit numbers and you say to your self multiplies the units digit if one times the units digit is another, write down something, let's say 37x23 if I can remember the, multiply 3x7, right down the line, carried it to, you go through a process and the process can be automatic and you can get it right and get the answer. And that's a favor, real favor to somebody who has to do it all the time. What it doesn't do though is serve education well in the reason is that I should save the beginnings of education well, the reason is that it's hiding the thinking and it's deliberately hiding the thinking so that when you are doing lots of computation you don't have all the thinking which causes you to make errors, the cognitive load. But for the youngest ones, you want to actually see what they are doing. So if they are multiplying what did I say 37x23, you would want them to say 3x7, that's 21, right down to 21. 3x30, not 3x3, 3x30, after all they did read it as 37, 3x30, right down to 90, so write down all that stuff. And algebra when they get to algebra that the only thing they will be able to. There is no such thing as carrying when you are multiplying X. times Y.
MAUREEN CAVANAUGH: Exactly right now let me take a step back because we have a caller on the line, if you could tell us what is your definition Dr. Goldenberg of algebra and why is it important that kids learn it.
DR. DAVID GOLDENBERG:The definition of algebra I kind of want to stay away from that. We had a discussion that lasted 10 years. So there are lots of different algebra, their school algebra, there's algebra the discipline, there's algebra course, there's a thing called early algebra which is why little kids do, there's algebraic thinking, College algebra. Too many different things. But the basic, the big deal part of it and especially if we are thinking of kids going to high school and taking the subject that's got a name, called algebra, the big deal part of that is not just the letters, it's that suddenly you're doing, you know you are doing arithmetic with these mysterious quantities that you don't even know what they are. But that the symbols are describing a calculation more than calling for. When you see 3+5 you say to yourself, you're almost it's almost screams to you to say eight. But when you say 3+ X. a lot of kids coming to algebra and say so what is the answer. Well, there isn't one. That's a description of a calculation that you could perform when you know X., or maybe in some circumstance you can figure out expert but for now I just says this is an addition problem, 3+ something and you'll figure out later what that something is.
MAUREEN CAVANAUGH: Principal Sciarretta, when kids are learning things like fractions and teachers say you know, what is that, don't ask why, just invert and multiply, that kind of thing it really does help a lot of kids do well on tests. But, David went in move on to higher mathematics it doesn't actually seem to serve them very well, is that what you've learned?
DAVID SCIARRETTA: Yeah, and I'm certainly not an expert in this, but that is anecdotally what we have learned. And also it doesn't have meaning, it is not connected to the real world, just manipulating figures for the purposes of going through a lockstep procedure. To come up with the right answer and be done with it.
MAUREEN CAVANAUGH: How did it occur to you and principal fund that indeed this may not be just an algebra problem, but it was a problem the larger way that math was being looked at and taught?
DAVID SCIARRETTA: Well you know this decline in math achievement in middle school is not something that is unique to the Einstein Academy's obviously, so this is a systemic thing. And we have a unique opportunity where we are because about 80% of our middle schoolers come from our elementary so adjusted to reason that we would kind of look back a few years and see, at least take a look and see how math was being taught and we have also very unique program in our elementary school which is a German immersion program so not only do we have, not only do the students with math standards in English but half the time they are leading them in German so we really had to peel this onion and come back and also have a look at the way that many of our teachers are from Germany as well in elementary school so what approaches today has an interestingly they actually had been taught in a very kind of problem-based weight, problem solving which is what we are moving toward in our middle school. But yes, we knew that we could not take the simplistic approach
MAUREEN CAVANAUGH: And just blame it on algebra.
DAVID SCIARRETTA: Yeah, that's right I mean in society we like to do that. We, I think being a math teacher is a really tough thing because the face kind of this general math illiteracy that is accepted people tell you they can't balance a checkbook educated intelligent people tell you they never tell you that they couldn't find a way to house because they couldn't read the signs on the freeway. So our math teachers have this incredible burden that is in addition to what other teachers and other disciplines is because it is the algebra you know, the boogie monster.
EMILY ALPERT: One of the most beautiful things that one of the elementary school teacher said to me is that they look at math as a third language. So English, German and math.
MAUREEN CAVANAUGH: Well that brings me to my question Emily, how surprised were these teachers did you hear from them when they found out the note that if you asked a formulaic problem in another way that it just really didn't make any sense to these kids and therefore they weren't really understanding the basic concepts of math and arithmetic that went along with the original formulas?
EMILY ALPERT: I think I mean at least I heard from a couple of the teachers and the principal it was pretty surprising because the way our tests are written they reward them, they reward kids for not thinking and so to sit down and say something like what is 9/10+35/36 and the kids would want to sit down and start actually figuring out the common denominator. Instead of just sitting back and saying 9/10 is almost 1, 35/36 this almost 1 so it must be almost two. It's funny the whole conversation we are having this sort of eerie because last night I was helping a seven-year-old with her homework and she was adding two 2 digit numbers and she was adding the tens place to the ones place because she had learned this algorithm she learned a series of steps and she messed up one of the steps. So I sat down with her and said why are we adding that one and that one and she couldn't tell me. So it's very common unfortunately that we sort of teaching math as a series of shortcuts and not as a way of thinking.
MAUREEN CAVANAUGH: I'm talking with reporter Emily Alpert and principal David Sciarretta and Dr. Paul Goldenberg who is with the educational development Corporation. We are talking about a mask curriculum that's been introduced by the Alpert Einstein Academy which is a charter school here in San Diego and we are talking about teaching math and getting kids to continue their love affair with numbers long, beyond algebra. We are taking our questions at 1-888-895-5727. We have to take a short break and when we returne we will continue our discussion. You are listening to These Days on KPBS. Welcome back I'm worried Tonight you're listening to These Days on KP BS. My guests are education reporter Emily Alpert to voice of San Diego.org principal David Sheridan of the middle school of Alpert Einstein Academy and Dr. Paul Goldenberg who is distinguished scholar of teaching and learning at the educational development Corporation. And we're talking about the new ways of teaching math especially higher forms of mathematics to kids in a way that is smaller, focused on problem solving and doing formulaic solving of number problems. 1-888-895-5727 is the number to call. And Dr. Goldenberg I want to, what we just talked about ego, and why kids are learning algebra in school, in middle school I was always taught when we would complete in school that we were being taught this mathematics because it was going to help us think logically when we were older. Is that still the end?
DR. DAVID GOLDENBERG:Well, part of the reason for learning algebra now is pretty pragmatic actually. It's for right or wrong, it is a ticket for more of the education that gives you to to have reasonable and reasonably lucrative choices for work it is a ticket to college. But yes absolutely if algebra, mathematics can be taught in ways I really do improve your thinking. And this is exactly the discussion that you are having. It can also be taught as a bunch of steps to take, things to know, rules to memorize and those arguably don't, you know, that's not improving your thinking, that's just more things to know. If it is time as logic, if it's actually based on the kind of natural smarts and they come with a whole lot that we are not really using them it's a great playground, a great exercise gym for developing better and better thinking that people use in all sorts of places even if they happen not to be using the particular techniques of algebra.
MAUREEN CAVANAUGH: Great so when kids are told to look at a particular problem and that perhaps there is no single way to solve this problem, that's the kind of thing that might intrigue students but might give parents the willies.
DR. DAVID GOLDENBERG:Yeah, I think also that well, you know there is a way to solve the problem and one could specify that, but the business of reasoning out, puzzling out how to solve problems, I don't think that should take the place of learning some you know, some nice techniques sometime, but that's a very important part of the diet. If you're going to be a doctor or a car mechanic you are going to be faced with vaguely described problems and you don't want to disassemble the entire car, you want to zone in on the most likely candidate. You want to use the clues you've got and make a thing to fix. I might also add that you know, law school admissions tests has on at the kinds of puzzles that we have a tendency in school to reserve for a rainy Thursday afternoon. But they could, they are not the desert. If you are thinking of sending your kid to desert, to law school they are the main course or at least part of the main course. Eric but important vegetable along with whatever else you are eating.
MAUREEN CAVANAUGH: We are taking your calls at 188-895-5727 let's hear from Ari. He's calling us from Northpark, good morning, Ari, welcome to These Days.
NEW SPEAKER: Thank you for having me on. I'm a University math professor and I really applaud what you are doing because I find a lot of my students even a really great University do not have the sort of basic algebra skills that I would expect them to have. And in fact to a great extent there is a big movement in calculus reform to sort of do an end run around in algebra and kind of make it more formulaic. And I think that's entirely the wrong direction to go. Anyway, what I'm curious about is whether you've gotten any pushback from parents because I know whenever there is a reform movement in elementary mathematics even going back to the new math during sort of the Cold War era a lot of parents would complain that they didn't, they couldn't help their children with their math homework, they didn't recognize the problems. Have you gotten any parental pushback
MAUREEN CAVANAUGH: Principal Sciarretta, I'm going to give that to you.
DAVID SCIARRETTA: It's a great question. We have had some parental let's just call it high interest and I think that's a good thing that comes anytime in the area of Matthew elementary school has begun a series of parent education evenings to really walk parent step-by-step through what our new math adoption in the elementary grades looks like and we are planning those as well in the middle school. And being to charter schools I think just inherently parents tend to be more open to change and innovation. Which is a good thing, but everyone wants what's best for their kids so I have had parents come up to me and very open-minded parents and say but when is the real math coming and you know, so most of us weren't time from a conceptual standpoint, from a problem-solving standpoint I think it inherently as little kids that's the way it we thought and that it was taught out of us. It's a great question I have to applaud our general school community that we have parents who are on board with something that is really focused on thinking because that's what we are about the Einstein academies.
EMILY ALPERT: I have to say it's probably the only school that I've seen on that has on his home page the fact that they switch to a new math curriculum that gives you the sense that it is a big change. One of the parents I spoke to he has likened a first grader and he made mention the kind of problems his son was bringing home for math homework almost look like sudoku problems where you have to reason out the answer as opposed to just sort of the list of equations to finish. And he is a microbiology professor and he is, you know he's a pretty savvy guy but he said there was a couple times when his son came up with a sheet of homework and he would look at it and say how do you do that so it is a shift.
MAUREEN CAVANAUGH: And Dr. Goldenberg would they say nothing succeeds like success and I wonder how much this think math program has had in our school world today that is so emphasized so heavily emphasizing school test scores.
DR. DAVID GOLDENBERG:We are a little young, so I don't have cross the country kinds of data, but we've been watching some very successful schools, actually the first two that we were able to follow closely they are naturally nearby that's how we followed them closely, are two schools that were failing, one of them had been failing AYP for so long that it was about to be taken over and the other one wasn't doing quite so badly but it was also not making AYP. And I have to say to our astonishment you know I like the result but I wasn't expecting it. The first year that it turned around. It certainly would cause not just because of a change in program it was because the teachers got excited. They found something that interested them and they really worked at it very hard. But it showed with the kids. It asked the kids to do things and there was developmentally I mean, we paid a lot of education development Center paid a lot of attention to the child cognition. So it worked. It was pretty good.
MAUREEN CAVANAUGH: I'm sure at Einstein Academy is it too soon to tell.
DAVID SCIARRETTA: I'd say it's too soon to tell at all the elementary and where we have the middle school where we have college preparatory mathematics but anecdotally that teachers are again very excited and that's huge. In the middle school we actually has a staff meeting two years ago that teachers got together and said you know we need to support our math team. So as a staff we came up with a math problem of the day that happens across the curriculum, across the grades in every classroom at the same time that's based on, that's always a problem that a student has to approach from multiple perspectives. So we really have this kind of current of excitement about method really kind of mutual support and solidarity around improving students' understanding.
EMILY ALPERT: I wouldn't downplay results too much either. You guys saw a big jump in algebra scores at the same time. It is just a year but it is pretty striking.
DAVID SCIARRETTA: It's a journey
MAUREEN CAVANAUGH: I want to see if we have time for a couple calls. Sandra is calling us from San Diego good morning Sandra, welcome to These Days.
NEW SPEAKER: Hello.
MAUREEN CAVANAUGH: Hi.
NEW SPEAKER: Hi, I was calling because I remember when I was in school they used to take a long way around things and they have you focus, work on it for six weeks and you are bored by the time you finished and to me they bored the children out of wanting to learn. And when I got to the 12th grade I had one subject left so I decided to take my GED and when they gave us their math solutions it was like what I always did and not long and drawn out. I was really frustrated. I said why would they frustrate you to death in school and not use something that's exciting.
MAUREEN CAVANAUGH: Well I think that's part of what they are trying to do here with think math and Sandra thank you so much for the call. Robin is calling us from San Diego. Good morning Robyn welcome to These Days.
NEW SPEAKER: Good morning, thank you for taking my call. I wanted to say that when I was in high school I had an affinity for literature in English and writing so I was placed in an advanced placement program for English which at that time included advanced placement for math. And I was terrified by math throughout my whole education. But, so I avoided math classes and I took as little as possible, but I landed into a college in California where a professor and as ridiculous as it may seem, put a picture of the bridge with it an equal sign underneath and said a magic troll is going from this side to this side, both sides have to be equal, so at the time I was furious. I thought I'm in college, why is he talking to me about trolls on bridges but when I thought about it later if suddenly became completely clear and from that moment, algebra became simple to me in the sense that it's just a matter of equalization, solving problems. And I was able to go on in math studies that were actually quite interesting to me and I wasn't terrified anymore. So since you guys were talking about teaching methods, sometimes it needs to just, I believe it needs to just be brought down to the basics because a lot of people in math are terrified.
MAUREEN CAVANAUGH: Right, Robin, thank you so much for the call I really appreciate it. Dr. Goldenberg that kind of conceptualization is exactly what you are talking about isn't it.
DR. DAVID GOLDENBERG: Actually wanted to respond to Sandra's first comment it's absolutely true, Sandra also mentioned why would you go so slow and you would bore the kids. One of the things that we've seen obviously I don't want to raise the corset if you are rushing to cover content and leaving the kids behind they're not learning anything but one of the things we've seen is when kids are having trouble there's a tendency to slow down and do some of the time that may be strategically right, but some of the time what's happening is just try to imagine your favorite piece of music played at a quarter of the speed. You wouldn't recognize it, and you wouldn't understand it and you certainly wouldn't like it. You don't hear that way. You know, if this were not a radio program I would say what if I come I would slow down the speech, you can understand that. They sometimes actually helps kids who are struggling to pick up a lively pace. You will be watchful, watch, make sure they are not getting lost, but actually pick up the pace so that you can see the picture better. And you know, keep it lively for them.
MAUREEN CAVANAUGH: Put some zaz into it.
DR. DAVID GOLDENBERG:Yeah, it's not just the entertainment, it's what the mind latches onto. We do fall asleep if things are going too drearily.
MAUREEN CAVANAUGH: Now, Emily as part of wrapping up your piece you talk about the San Diego unified school district actually thinking about doing some modifications to the way that it teaches math. Tell us about that.
San Diego unified introduced some new math textbooks this year they are called innovation math and the idea I don't know that the concept is completely the same, but it's also clear that adjusting elementary math education to help algebra. So the idea is to introduce algebraic concepts earlier to actually call them algebra earlier. So in each level there is something that says you know, this is the algebra link for whatever this lesson is. And it's just been introduced this fall and some teachers are still getting trained on it, so the jury is still out. But it shows you that there's a lot of interest in renewing the whole way that math is taught and to better prepare kids for algebra.
MAUREEN CAVANAUGH: And they might think of a picture with the bridge because we know that that at least helped one person a lot. I want to thank my guests so much. We are out of time. Emily Alpert, thank you.
EMILY ALPERT: Thank you.
MAUREEN CAVANAUGH: Principal David Sciarretta, thanks for coming in,
DAVID SCIARRETTA: Thank you, Maureen and it's been a pleasure talking with you.
MAUREEN CAVANAUGH: Dr. David Goldenberg, thank you so much.
DR. DAVID GOLDENBERG: It was a pleasure talking with you.
MAUREEN CAVANAUGH: We didn't have time to get everybody's question on here so if you'd like to be like everybody to go online at KPBS.org/These Days with your comments and stay with us for hour two of These Days is coming up in just a few minutes you are listening to These Days on KPBS.