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Mastering algebra is widely considered a stepping stone to higher mathematics and college readiness. But last month, a political science professor touched off a debate when he challenged the value of algebra in American education. He argued we should remove algebra from high school and college curriculum, citing it is a key reason why kids drop out of school. But critics say the issue is not algebra – it’s how it’s taught. With more effective class instruction, the course can instill critical thinking and reasoning skills needed in everyday life. Diane talks with her guests about math education and why it matters.

- Judy Bolton-Fasman a writer and parenting columnist.
- Jacob Vigdor professor of public policy and economics at Duke University.
- Ed Nolan program supervisor of mathematics in Montgomery County.
- Andrew Hacker professor of political science at Queens College of New York. He is the co-author of "Higher Education? How Colleges Are Wasting Our Money and Failing Our Kids - And What We Can Do About It."

#### 11:06:56

MS. DIANE REHMThanks for joining us. I'm Diane Rehm. Last month, Professor Andrew Hacker of Queens College questioned the role and value of learning algebra. He says the course is a stumbling block for many students, and hurts both high school and college graduation rates. But critics argue algebra is essential for learning critical thinking skills needed in everyday life.

#### 11:07:24

MS. DIANE REHMJoining me to discuss the pros and cons of teaching algebra, Andrew Hacker, professor of political science at Queens College. Ed Nolan, program supervisor of mathematics in Montgomery County, Maryland, and from a studio in North Carolina, Jacob Vigdor, professor of public policy and economics at Duke University. I hope you'll join in the discussion as well. Call us on 800-433-8850, send us your comments on the important topic to drshow@wamu.org. Feel free to follow on Facebook and Twitter. Good morning to all of you.

#### 11:08:11

GROUPGood morning.

#### 11:08:13

REHMAnd good morning and welcome to all of you. Professor Hacker, you wrote on op ed for the New York Times last month. It was titled, "Is Algebra Necessary," and in the piece you suggest that algebra should not be required curriculum for all students. Tell us why.

#### 11:08:45

DR. ANDREW HACKERAll right, Diane. We have approximately, let's say, four million 14-year-olds in this country. Every single one of them is required, expected to take this subject called Algebra, and I regard -- and by the way, most of them find it difficult, very difficult. Some people have a gift for math, but most of us don't. Now, the question is -- and by the way, algebra is the largest single academic reason why students don't complete high school. A national disgrace is that 25 percent of our ninth graders don't make it through to a diploma.

#### 11:09:26

REHMHow do you know that that particular subject is the reason?

#### 11:09:34

HACKERFrom talking with teachers. We don't keep -- we don't track this.

#### 11:09:38

REHMYeah, exactly.

#### 11:09:39

HACKERStudents have problems with reading...

#### 11:09:41

REHMSure.

#### 11:09:41

HACKER...of course, and notice I said academic reason. I'm not talking about family ones. And it's fairly simple. Algebra is a much greater boulder to push up a hill than let's say reading "To Kill a Mockingbird." In all event, what is happening is that we're wasting a tremendous amount of talent because people are not finishing high school, not finishing community colleges, even not graduating from college because of math requirements. And I suggest -- I'm suggesting we rethink this compulsorily required subject. But maybe make it an elective.

#### 11:10:23

REHMAnd to what extent would people be able to negotiate fairly straightforward skills in life if they did not have algebra?

#### 11:10:43

HACKERThat's a fair question. I am all in favor of quantitative literacy, quantitative reasoning, being able to deal with statistics. For example, one candidate says the health care act will bankrupt us. Another candidate says, no, it will benefit us more than ever, you know, pay for itself. The citizen has to be able to handle those figures. That doesn't require algebra. It really requires just facility with numbers up through proportions, ratios, fractions.

#### 11:11:17

REHMAndrew Hacker, he's professor emeritus of political science at Queens College of New York. And turning to you, Ed Nolan, you are currently supervisor -- program supervisor of mathematics in Montgomery County, Maryland, but I gather you have taught in the middle school and high school level for 19 years. Why do you believe that algebra is important for students' curriculum?

#### 11:11:55

MR. ED NOLANThe importance of algebra has a lot to do with the way it facilitates thinking for students, for all of us. The way it allows us to see the world through a particular lens, how it allows us to see patterns in the world. How it allows us to represent those patterns in different ways. Dr. Hacker talks about the desire to have quantitative reasoning. I completely agree we need quantitative reasoning. I don't disagree with that at all, and it can be used to facilitate those views that are part of algebra.

#### 11:12:28

MR. ED NOLANThe ways of predicting what's going to happen in the future, seeing those patterns, being able to represent those patterns in multiple ways, being able to communicate those patterns across cultures, because mathematics is a language that is consistent many cultures, probably as consistent as any other. So that all of those different representations, abstracts, symbolic, allows us to see those generalizations. Those generalizations are how we are able to interpret the world around us.

#### 11:12:56

REHMBut could you skip over algebra and get to the rest of what you need mathematically to negotiate the world?

#### 11:13:10

NOLANI'd -- to be successful in negotiating the world, I don't think so. Can you negotiate the world without algebra? It is possible. But do you have doors closed because you don't know algebra? And that would be one of my concerns is, is if I know...

#### 11:13:22

REHMWhat kinds of doors?

#### 11:13:24

NOLANTo me, it would be those doors that help where predictions are necessary. Where I'm trying to figure out what the world is going to be like. If I'm a stock analyst, I need algebra because I'm looking at patterns. I'm looking the way patterns grow. Are they growing consistently? How much change is there? What kind of variance do I have?

#### 11:13:43

REHMAnd can one argue that if you're going to be a stock analyst and you care about mathematics, you care about algebra, and then you work towards it. It's part of what you want to do.

#### 11:13:59

NOLANAnd as Dr. Hacker talked about, there are 14 million 14-year-olds, and I knew when I was 14 I was going to be an architect, and so I didn't need a great deal of math. I needed a lot of art because I was going to be an architect and I was going to be sketching and drawing. But you know what, I didn't end up being an architect, and at 14, you may not know what you're going to do. And if you don't have these experiences, you may not be able to figure out what you really want to do.

#### 11:14:22

REHMEd Nolan, is program supervisor of mathematics in Montgomery County, Maryland. And turning to you now, Jacob Vigdor, as professor of public policy and economics at Duke University, talk about how educators' thinking about algebra has evolved over time.

#### 11:14:51

DR. JACOB VIGDORWell, I think the evolution is kind of represented by what we've heard so far. So there's one school of thought that says we need to be very practical in math education. Algebra is a very abstract subject, and there a lot of lines of work where you're not necessarily going to use it every day. But on the other hand, there has been this other school of thought to say we really need to focus on building fundamental skills which means making sure that everybody gets the fundamental concepts as abstract as they may be.

#### 11:15:22

DR. JACOB VIGDORIf you look back to the era up to maybe World War II with the 1950s we were pretty content with allowing most students to avoid algebra, geometry, trigonometry and some of those more difficult subjects. But then, you know, around the time of Sputnik and the new math movement, we sort of decided that it was important for a broader segment of the student population to have access to these courses. But what we've discovered over time, is that we haven't really figured out a way to offer these courses to people in a way that they master the material on a schedule that we'd like them to master it on.

#### 11:15:59

REHMSo I don't quite understand what that means. Is it that it becomes too advanced too quickly for the 14-year-old mind, for example?

#### 11:16:12

VIGDORI think that there a good amount of truth to that. If you look at the way we taught algebra 60 years ago, it was considered to be tenth grade material, and now, in a lot of parts of the country, most eighth graders are taking algebra, and in some cases, even seventh graders are taking algebra. There are gonna be some students who are ready for it at that young age, but I'd say that for the average student, eighth grade is asking them to take this subject matter before they've really had enough of a chance to make sure that they've solidified their grasp of the materials that underlie it.

#### 11:16:47

REHMWhat about that, Professor Hacker?

#### 11:16:50

HACKEROkay. My basic question is, why are we making every student take algebra? And, by the way, various myths and mantras grow up around a subject like this. For example, the notion that algebra somehow enhances, sharpens your critical thinking skills. Total myth. Let me take this, let's suppose over here are 10 people who have mastered algebra, and another 10 over here who have not. Are you going to tell me that the people who have mastered algebra have better thinking ability, are more thoughtful about politics, society, have better marriages, make better decisions about what we should do with a country like Syria.

#### 11:17:39

REHMAll right. Ed Nolan, can you answer that?

#### 11:17:45

NOLANIn part, it's going to be how did the students experience algebra, and I think that's one of the critical questions that is embedded within this, is what is algebra? Is algebra a set of rules you identified, Dr. Hacker, in your op ed piece about squaring the sum of X squared plus Y squared and whether that was valuable. As an individual example, it's not value. As a reasoning skill, can you see how to break apart -- can you see the components that make that up? Can you view it through different lenses, can you look at it as a graph?

#### 11:18:14

HACKERAnd do you have any evidence -- evidence that people who have studied and mastered algebra are more thoughtful than people who have not?

#### 11:18:22

REHMHold that thought, Ed Nolan. When we come back, you can respond. What a fascinating conversation. I did take algebra in the eighth and ninth grades. I took it again, first year at American University. We'll be right back.

#### 11:20:04

REHMAnd welcome back. We're talking about the debate over the teaching of algebra. Andrew Hacker is here. He's professor of political science at Queens College of New York. He wrote a piece for the New York Times which was published last month saying, "The course is a stumbling block for many students and hurts both high school and college graduation rates."

#### 11:20:39

REHMAlso here in the studio Ed Nolan, program supervisor of mathematics in Montgomery County. On the line with us from Duke University is Jacob Vigdor, professor of public policy and economics at Duke University. Ed Nolan, just before the break, Dr. Hacker asked you a question. Can you answer?

#### 11:21:05

NOLANThe question had to do with whether a student who was successful in Algebra would have better critical thinking skills -- and I'm turning to Dr. Hacker to make sure I'm getting the correct question -- would have better critical thinking skills than students who are not part of algebra. And to me it would be is the algebra that that student -- that that person learned, was it a valuable course? Did they look at real life situations and how algebra plays its role in that?

#### 11:21:32

NOLANDid they look at different car rental rates, for example, to figure out what would be the better deal if I'm going to rent a car for four days or for five days? Were they able to take a problem, break it down to its components, see rates of change, see how things grow, be able to make predictions based on the overwhelming trend of the data? Being able to do that, to me, is representing algebraic thinking.

#### 11:21:56

REHMAll right. Now turning to you, Jacob Vigdor, if I have simply skills in addition, subtraction, multiplication and division will my critical thinking skills be as good as one who has had, say, two or three years of algebra?

#### 11:22:24

VIGDORWell, I'd say that if you did well in that algebra course and geometry and courses that followed up then...

#### 11:22:31

REHMI hated them. I have to tell you, I hated them.

#### 11:22:36

VIGDORYou might've hated them, but they didn't -- I'd say it's hard to argue that it makes somebody worse off to have mastered those skills. I think the issue...

#### 11:22:44

REHMThat's fair.

#### 11:22:44

VIGDOR...is that we're giving people the courses, but they're not mastering the skills. And so the -- you know, the main issue is that we have to figure out a better strategy for trying to educate people in these skills. Let me give you a very specific example...

#### 11:22:58

REHMSure.

#### 11:22:58

VIGDOR...of something that most people do where algebra, beyond basic, you know, arithmetic comes in handy. It's mortgages, okay. Mortgages are very complex financial instruments. If you want to calculate the value of the stream of payments that you're going to be paying over a 30-year mortgage or anything like that, you're trying to decide whether it's a good idea to refinance or not, all that sort of stuff, that's more complicated than just doing math, addition or multiplication.

#### 11:23:26

VIGDORAnd what do we see over the past ten years in this country? We saw that a lot of people got into trouble because they took out mortgages they couldn't understand. And then the bill for those mortgages that had to be bailed out falls upon the rest of us. So I think there is a case to be made that there's a public interest in having the type of consumer that can understand one of these relatively complex instruments.

#### 11:23:50

VIGDORAnd, you know, when you give people this sheet of paper that says here's your interest rate, here's what your monthly payment is, we don't want people to sort of have their eyes glaze over and say, you know, I trust you that these numbers are right. Because the person at the other side of the table has a vested stake in making the loan and not necessarily a stake in having the person understand the loan.

#### 11:24:11

REHMProfessor Hacker.

#### 11:24:12

HACKERDiane, in all good spirit, what we've just heard about mortgages is the kind of example you get from people who will use any rationalization for algebra. If you had a really complicated mortgage and you had started algebra, you wouldn't sit down at your kitchen table by yourself and try to work out this. You would go to a financial advisor and say, hey I got this 15-page mortgage document. Will you help me with it? Your 7th grade, 8th grade work in algebra wouldn't have helped you at all on this.

#### 11:24:46

REHMAll right. But here is another though from Peter who says, "The national disgrace is that American students are not prepared by the educational system to adequately master algebra. Mathematics is essential to complex thought and effectively manage the way through life, whether or not algebra itself is employed. Giving kids a pass on this because it's hard or does not come easily is counterproductive to our future." Ed Nolan, what's the problem with teaching algebra?

#### 11:25:36

NOLANA lot of the struggle in teaching algebra and in learning and being prepared for algebra is having the understanding of number. Dr. Hacker talks about wanting number to be the focus. Before algebra you have to understand -- too many of us have learned mathematics as a rule instead of understanding mathematics as a concept. When we only understand a rule we mix those rules up. We multiply instead of add. Talking about negative numbers, students always mess those things up because they don't understand the concept. They've learned it as a quick pneumonic instead of understanding what's going on with the number.

#### 11:26:13

REHMSo who's to blame for that?

#### 11:26:16

NOLANI don't know that I'd like to assign blame. What I'd like to do is talk about how we can improve it, how we can talk about trying to have more manipulatives, have more concrete experiences, have students actually experience the mathematics instead of learning it -- trying to learn it off of worksheets.

#### 11:26:30

REHMJacob Vigdor, is there a way to improve the teaching so that algebra does not turn kids off and they don't as a result, as Professor Hacker suggests, drop out of school?

#### 11:26:49

VIGDORI think the key is to change our strategy. If you look at what's happened, algebra used to be a 10th grade course, now we're pushing it in 8th grade. Our philosophy has been to try to hurry up. I think instead what we need to do is slow down, that we need to allow students to take the time to make sure that they're comfortable with some of the more basic mathematical concepts. They need to really get fractions before we pass them on to algebra.

#### 11:27:14

VIGDORThere's some good evidence now coming out of Chicago, for example. They had a program where they had students take algebra in 9th grade. They gave them twice the time to spend in the course. So they took it for two periods a day rather than one period of time.

#### 11:27:26

REHMInteresting.

#### 11:27:27

VIGDORAnd the students who participated in this program did much better on the course. So instead of trying to get people to get to this complicated subject matter when they're younger, take the time to make sure that they've got the fundamentals down. It's okay for it to be a 9th grade or a 10th grade, or even an 11th grade course if that's when students are ready to take it.

#### 11:27:47

REHMAll right. Before we get to the subject of job selection, career selection I want to read this email from Marry who says, "I somehow got out of math after having the same sorts of trouble your guests suggested with algebra. But now at 28, I regret it every day. Not being exposed to logic in that way I can almost feel that part of my brain shut off when I encounter even non-mathematical problems. Now almost 30, I find myself getting out my old remedial math books to help me think more creatively now. I would argue it's not math, but the way we teach it." Ed Nolan.

#### 11:28:45

NOLANWhat a wonderful story and a wonderful support of why it's about the ways of thinking that math supports, not just the pure mathematical examples. It's how do we foster that creative, that looking at problems and solving it. It doesn't have to be a specific algorithm.

#### 11:29:04

REHMBut what would you say to Jacob Vigdor's suggestion that perhaps we need to do it in different ways, maybe two years instead of three or whatever?

#### 11:29:21

NOLANI think what we need to do is -- I've written down the Chicago study because I'm going to -- I've got to research that because I agree. We need to have students ready for whatever we're going to offer them, whether it's algebra, whether it's geometry, whether it's a statistics course. We need to make sure we prepare them well for what they're going to do next. If it's more time, that's the way to go.

#### 11:29:40

NOLANThe only thing I'm concerned about is what are we losing from what -- you know, a student taking two periods of math every day means they're losing something else. And I'm always struggling with I would love for them to take math all day. That's a personal story. But I always want to make sure that students have a well balanced schedule because one of the things that might be why they would be dropping out is they're taking two periods of math. Maybe they need two periods of language arts. All of a sudden they don't get to do the art class, they don't get to go to do some of the things that they really enjoy.

#### 11:30:08

REHMProfessor Hacker.

#### 11:30:09

HACKERHere's what I'd say to Mary. Fine, I'm glad your education is continuing, as it will throughout all of your life.

#### 11:30:17

REHMGood.

#### 11:30:19

HACKERPlease do not assume that you have to go to a math book to sharpen your mind. You can read "Emma Bovary." You can read "The Great Gatspy." You can take a course in anthropology. Math is not the key to a sharp mind. And, in fact, I'm really believing more and more that the kind of thinking skills that math encourage are really constrictive because there's a very cold logic to math, whereas if you study anthropology you'll discover there are much more variation in the world.

#### 11:30:56

REHMBut let's move then to the subject of jobs and employment and how much employers expect a potential employee to be math literate, Professor Hacker.

#### 11:31:15

HACKEROkay. Just down the road the Georgetown University center on the workforce is the foremost research organization looking at what jobs will be needed in the future. And they're projecting up for the next ten, twenty years and their projection is only 5 percent of the workforce will need algebra and above. Only 5 percent and this is in our high tech time.

#### 11:31:44

HACKERThe question then is, is classroom algebra a key even for that 5 percent? And more and more research shows that there's a real disconnect between classroom algebra and what's needed in the workplace. I'll give you one brief example. Take Toyota, which makes a sophisticated car with a lot of electronic add-ons and so on. It recently opened a plant in rural Mississippi where the school district is far from stellar. Only 7 percent of the kids take AP courses there. But Toyota went there because they said we want reliable workers. Hey, some of them have to do math.

#### 11:32:27

HACKERSo Toyota made an arrangement with the community college which now teaches -- are you ready -- machine tool mathematics for Toyota. Okay. We can do that for those people who need it.

#### 11:32:42

REHMAnd without math skills.

#### 11:32:45

HACKERWithout classroom math skills at the age of 14.

#### 11:32:49

REHMAndrew Hacker. He is professor of political science at Queens College of New York. And you're listening to "The Diane Rehm Show." We have many callers on the phone. I'm going to open the phones now, 800-433-8850. First to Royal Oak, Mich. Good morning, Marie. You're on the air.

#### 11:33:19

MARIEWell, good morning. How are you?

#### 11:33:20

REHMI'm fine, thanks.

#### 11:33:22

MARIEWell, so my brief story, I was really horrible at math and I forgot about math after long division. High school, I hated algebra. My mother got me out of it, sure I wouldn't need it. But I went to college. When I got to college of course my mind was opened and I fell in love with soil science and I fell in love with landscape architecture, both of which require math skills. And so I had to decide, should I choose my -- you know, follow my love or -- and face my math demons or do I forget about it because I don't know math?

#### 11:33:55

MARIESo I decided to follow my dream and I had to get math tutors and I had a great professor named Max Benny. But I always regretted that they didn't somehow make it -- make math easier for me in high school. So maybe it's not an either/or. Maybe you don't have to get As and excel in algebra in high school, but you should at least understand the fundamentals so that you're not starting over again when you are 25 years old.

#### 11:34:22

REHMProfessor Vigdor, do you have a comment?

#### 11:34:25

VIGDORWell, you know, I think that it's -- we had some comments earlier along the lines of when you're 14 or 15 or 16 it's hard to forecast exactly what you want to do when you grow up.

#### 11:34:38

REHMQuite right.

#### 11:34:39

VIGDORAnd there's something to be said for keeping your options open. And the more skills that you acquire the more that your options are going to be. You know, professor Hacker's comment that only 5 percent of jobs are projected to required algebra, what kind of jobs are in this country depends on what kind of skills our workers have. And if we have workers who aren't good at math of course we're not going to have jobs that require math skill because there'll be nobody qualified to take them.

#### 11:35:02

VIGDORIf we do something to upgrade the math skills of our work force, then we'll have a phenomenon where more of the math intensive jobs will be here rather than shipped overseas, you know, to India or wherever it is in the world where they do math better than we do here.

#### 11:35:14

REHMAnd here's an email from Loke -- sorry, Luke in Caledonia, Mich. who says, "I've been waiting for someone to say this for years. We do not require a math-minded person to take woodshop so why would they require a woodshop expert to do the opposite? There are kids who are brilliant in many things like English, Art, working with their hands, et cetera, who are left out in high school and college or made to think they're stupid since they can't pass this meaningless subject." Ed Nolan.

#### 11:36:00

NOLANI knew you were gonna turn it to me. And for me, it's I see math as fundamental to existence and maybe that's my view of the world. But everyone's required to take a literature course -- you're required to read. You're required to know how to do that. Why wouldn't you also want to know how to do mathematics? Why wouldn't you also want to be able to think critically?

#### 11:36:24

NOLANI disagree a little bit with Dr. Hacker in the sense that I believe algebra does promote critical thinking when taught in a way around a critical thinking base.

#### 11:36:33

REHMAnd let me give you an absolutely opposite view, this from Victoria in Rochester, N.Y. She says, "Great idea and while we're at it, get rid of science, especially physics and chemistry, since they require some algebra and even higher math since that's pretty tough, too. Then we can drop history since kids hate all that old stuff. And finally, let's ax English since reading all those books and writing all those essays is pretty boring, too. Does anyone seriously believe that dummying down education is going to be good for us in the long run?"

#### 11:37:25

REHMAnd on that note, we'll take a short break. When we come back, we'll open the phones. We have lots of callers waiting. I look forward to speaking with you.

#### 11:40:03

REHMAnd welcome back. Just before the break we had an email about dumbing down education. Professor Hacker, what do you think about that?

#### 11:40:15

HACKERYou know, Diane, after I wrote this piece for The New York Times, my email mailbox exploded.

#### 11:40:23

REHMI can only imagine.

#### 11:40:25

HACKERRight. And they found my address and they got to me. And the biggest single charge against me was I was in favor of dumbing down the curriculum by getting -- and I have, you know, always wondered about that because a lot of people who did suffer through algebra, but finally mastered it, passed the course. And they kind of believe that annealed their character, you know, in a furnace. And therefore they want today's overindulged young kids to have to go through it as well. You know, well, perhaps. But what I'd say here is there are all sorts of ways.

#### 11:41:05

HACKERFor example, in a class I would propose in statistics where you have to decided which are various views on the costs of the healthcare law. You know, which is more accurate, what you hear from Mr. Romney or Mr. Obama? That is just as demanding as algebra, because you have to dig in statistics, you have to discuss motivations, all sorts of things like that. It's not dumbing down.

#### 11:41:30

REHMIt's very difficult. It's very difficult. And we're joined by Judy Bolton-Fasman. She's in Massachusetts. She's a blogger and writer on parenting and family life. Good morning to you, Judy.

#### 11:41:49

MS. JUDY BOLTON-FASMANGood morning, Diane.

#### 11:41:50

REHMYou wrote an article titled "In Defense of Algebra and Other Difficult Subjects." Why do you think learning algebra is an important thing to do?

#### 11:42:03

BOLTON-FASMANWell, listening to the discussion, I'm worrying that we're perpetuating a stereotype about math. And stereotype to some degree are incomplete. And I don't think it's necessarily true that algebra is beyond the grasp of most people, like some of your guests and your email correspondents have said. I think that it's a question of how we teach it, how we approach it. And if kids don't learn math and don't have solid math skills, they're going to be shut out of beautiful subjects like physics, like chemistry.

#### 11:42:40

BOLTON-FASMANAnd I think it's a lot to put on the shoulders of an eighth or ninth grader whether or not they want to continue with math. The brain development is incomplete until your 25. Like one of your email correspondents said, she's just going back to math now. And I'm saying this, I'm coming from this point of view as a person, as a math phobic, as a person who did anything she could to get out of mathematics.

#### 11:43:02

REHMSo how did you get over or beyond that phobia? Was it because of someone being a particularly wonderful teacher? What happened?

#### 11:43:17

BOLTON-FASMANWell, I can't honestly say that I'm completely over it, but I had children and my children inevitably went into math courses. And I don't pretend to be able to tutor them in math. They're far beyond me at this point in mathematics. But I wanted to see if I could challenge myself, if I could -- if I could learn math, if I was really just beyond help or I could really do it. And I went on a wonderful website called kahnacademy.org, which was founded by Sal Kahn. And he originally founded it to help his young nieces who were far away from him in New Orleans. I think he was in New York at the time or in Boston. And he made YouTube videos for them showing them how to do mathematics.

#### 11:43:58

BOLTON-FASMANSo I thought here's a subject I really hate and I was traumatized by geometry. And I went on and low and behold I decided I was going to do a proof with Sal Kahn walking me through every step of the way. Granted he is an amazing teacher. I was by the end solving SAT level geometry proofs. Does that make me a better person? No. Does that make me more of a critical thinker? I don't know. But it certainly gave me confidence. And I think math gives confidence particularly to girls. And it opens up worlds for them that weren't previously opened up to them, like engineering, like medicine, like if they want to do something in the -- you know, in the sciences or industry. So I think math is a very, very important skill set to have.

#### 11:44:49

REHMSo, Jacob Vigdor, let's turn for a moment to girls and math and educating girls first about algebra and then going on to physics and the like as Judy has clearly done and her children are likely to do. How important do you believe it is to encourage girls not only to do math, but to enjoy it?

#### 11:45:20

BOLTON-FASMANI think it...

#### 11:45:21

VIGDORWell...

#### 11:45:22

BOLTON-FASMANI'm sorry, (unintelligible)

#### 11:45:22

REHMGo ahead. No. I want Jacob Vigdor to comment.

#### 11:45:25

BOLTON-FASMANOkay. Sure.

#### 11:45:26

VIGDORYou know, there is a wonderful study by a friend of mine at Northwestern University that looked at the math performance of sisters, and sisters with different names, of course, as sisters generally tend to have. But he looked at situations where sisters had -- one sister might be named Barbie and the sister would be named Pat. So he was just judging the sisters by how feminine their names were. And what he found was that girls with more feminine names, they did fine in elementary school math, but as they went forward into middle school and high school math, they started to perform worse.

#### 11:46:03

VIGDORAnd it wasn't because of any difference in family background, because they came from the same families. It's because they were being treated differently in the classroom, because people were stereotyping them. And I think that it's important to recognize this, that this is something that's a really phenomenon. And I think, you know, one thing that I've learned in being an instructor, I mean, I've taught statistics classes here at Duke for many years, and students are not all equally adept at learning statistics. Some people need to learn at a slower pace than others. You really need to tailor the way that you teach this subject matter to the students that you're trying to teach.

#### 11:46:45

VIGDORAnd I think that that's, you know, that's one thing that we really have to keep in mind, that if we really want to encourage basic numeracy, basic proficiency with mathematics, whether it's lower level or higher level, we kind of have to acknowledge that people are different, that different people learn in different styles and they really get it in different ways.

#### 11:47:04

REHMAll right.

#### 11:47:05

HACKERJacob, just a second.

#### 11:47:07

REHMOkay. Go ahead, Dr. Hacker.

#### 11:47:10

HACKERI find myself -- Jacob, girls do better at math than boys do in classrooms. They get better grades in math than boys. This whole business about how if your name is Patsy, the professor won't pay attention to you is absolutely wrong.

#### 11:47:29

VIGDORWell, I can (unintelligible)

#### 11:47:30

HACKERIt's only on the SAT...

#### 11:47:31

REHMHold on. Hold on.

#### 11:47:32

HACKERIt's only on the SAT, that horrible multiple choice test that guys do better than girls.

#### 11:47:38

REHMAll right. I'm going to open the phones now and take a caller in Greensburg, Ind. Good morning, Everett.

#### 11:47:49

EVERETTGood morning. Good morning to everyone.

#### 11:47:51

REHMHi.

#### 11:47:53

EVERETTI just want to start out by saying, you know, I'm a double major. I've got a degree in business as well as a electrical engineering degree from a second university. I wanted to add that I would say that I'm more of the -- could be considered one of the slower learners in engineering where I took the engineering sequence on average each class twice. I basically persevered through the classes only because I had a desire to become an engineer. I want to reflect back on one of your guest's comments about the Toyota plant opening up in one of the southern states.

#### 11:48:25

EVERETTI myself currently work for Honda of Indiana where we produce Civics. The manufacturing floor and the assembly individuals who put together the car aren't really required to have that high of a skill set in terms of mathematics. I'm pretty sure Toyota does the same things because I have former colleagues that now work for Toyota and reflect the same as far as the skill set that's needed. I myself believe that mathematics is very, very integral. Yes, I maybe bias because of the fact that I'm an engineer.

#### 11:48:57

EVERETTBut I have yet to come across a facet in life, whether it's buying a car, buying a house or even doing just general grocery shopping or shopping for clothes where I don't look at, you know, sales, things of that nature, that are mathematical based. I believe if people aren't taught in terms of understanding the basis of mathematics in order to better themselves and/or control their finances, they can, in a sense, be taken, as the word was.

#### 11:49:26

REHMAll right. Thanks for calling. And, Ed Nolan, how do you respond?

#### 11:49:32

NOLANI certainly see the value of mathematics and certainly agree with Everett that mathematics is in the world around us. It's -- some of the conversation we've had has been about the student experience in the math class. It's the teacher's job to engage those students, to find ways to make those connections so that they do see the relevance of the mathematics. I agree. I'd love for math -- I'd for students to want to take math, to make an elective. But we have to find ways to make that mathematics engaging for the students for that to happen.

#### 11:50:01

REHMAnd, Judy, how important do you see your role as a parent and mentor to your children?

#### 11:50:10

BOLTON-FASMANOh, I think it's absolutely critical. In fact, in my article "In Defense of Algebra," I make a distinction between teaching and mentoring. Teaching actually is on the ground and teaches kids facts and gets kids through various problems and thinking strategies. And mentoring gives a more aerial perspective. And I think that's my job is to give my children a more aerial perspective and putting math in that picture and showing them how essential it is completing that picture.

#### 11:50:42

BOLTON-FASMANI also -- I don't want my kids to be, you know, tone deaf in a way either, in that I don't want them to think that -- math is the language of science and I don't want their math skills to go the way of language instruction has gone in this country. And that would make me very sad if they didn't have competency in math and, you know, weren't, so to speak, bilingual in math.

#### 11:51:04

REHMAll right. I'll take a caller from Chicago, Ill. Good morning, Kammy.

#### 11:51:12

KAMMYGood morning. Thank you very much for having me on with this conversation.

#### 11:51:14

REHMSurely.

#### 11:51:16

KAMMYI have been waiting for many, many years. I find that now I'm 25 years old. I'm currently in college going into about my second year. I never had any of the basic foundations of math coming from the inner city schools, whether it was a lack of resources, not having the books, not having the teachers prepared enough to teach us even the foundations. I find myself now being in Chicago in the suburbs in a better school and I find it very hard. I have taken algebra now seven times. I have failed it seven times. But I have always done exceptionally well in language and all the English classes. And I've even been able to maintain a very high GPA.

#### 11:52:06

KAMMYI do agree with Professor Hacker in the sense that there are other ways to learn some of the critical thinking skills and problem solving skills 'cause I excelled at logic even. So for someone like me in this position, what would you say would be a good route to take, maybe to even try something new? I've had amazing teachers, but I still find myself really struggling now that I'm older -- now that I'm older taking it.

#### 11:52:31

REHMVery interesting. Yeah, Professor Hacker.

#### 11:52:35

HACKERKammy, I really feel for you, that you took that course and failed it seven times. Something sadistic is at work here. It's really sad. Here's what I'd suggest, that mathematics departments both at high school and college offer alternatives, for example, a course in the history of mathematics. At DePaul University in Chicago, to pass a math requirement, you can take a course in history of math.

#### 11:52:59

REHMInteresting.

#### 11:53:00

HACKERWhy not that?

#### 11:53:00

REHMMm-hmm.

#### 11:53:01

HACKEROr the philosophy of mathematics. Galileo said, mathematics is the language of nature. Let's think about that. Let's have that taught. It's beautiful.

#### 11:53:13

REHMAnd you're listening to "The Diane Rehm Show." Ed Nolan, what would you say to Kammy?

#### 11:53:21

NOLANI'm so disappointed that you failed a class seven times. That overwhelms me that you would have that much perseverance and not be successful. I'm sure you've had great teachers. I agree with Dr. Hacker. I think you need to look at working with the university about finding another route because you've demonstrated you have the perseverance and it's just not there. I think a history of mathematics, a way that you can bring in the logic that you obviously do well with into the mathematics, the readings that you could do that would be wrapped around that. It seems like an independent study course would be most acceptable.

#### 11:53:52

REHMI hope you'll take some of that advice, Kammy. Good luck to you. And to Brett in Baltimore, Md. Good morning to you.

#### 11:54:01

BRETTYes, good morning, guys. Thanks a lot for having me on.

#### 11:54:04

REHMSurely.

#### 11:54:05

BRETTI'm 69 years old. And I guess I came along before they had classes like the history of mathematics. And I was like Kammy. I was -- I flunked algebra, I think, six times through high school. And then I got to college and it was a prerequisite to go on to graduate school.

#### 11:54:21

REHMOf course.

#### 11:54:23

BRETTAnd I just couldn't make it. And thanks to the mercy of one math teacher who called me into his office and said, I'm giving you a C because I have faith in you, but don't ever try to learn algebra again, and I did that, went on to get my master's and PhD. And if it wasn't for that, I could've never...

#### 11:54:41

REHMWow.

#### 11:54:41

BRETT...written my three books and I wouldn't have had a successful career. So I guess that would be my comment. I am all for the expansion of traditional academics. I think it's terrible what we're doing in our schools. But I think that one thing we need to do is not necessarily make certain things a prerequisite to be able to ascend, because we send -- I think we block off some really good minds that way.

#### 11:55:11

REHMJacob Vigdor, your comment.

#### 11:55:14

VIGDORSo, you know, when you think about it, we've heard from a couple of callers who have made this point that this is a hurdle that some people just have not been able to get over, and if they just find a way to sneak around it, they go on to do great things. And I'm sure that there are people out there like that. You know, when you get right down to it, there should be some flexibility, that we should find a way to get people to realize their full potential. We shouldn't put these hurdles in the way that prevent that from happening.

#### 11:55:43

VIGDORAt the same time, it sure would be nice if we figured out a way to -- rather than just sort of give up entirely and say, all right, we're just gonna forget about this, we're gonna accept the fact that American students can't do algebra, if we could actually figure out a way to make that not the case and find a way, in some cases, for students who are beyond high school now, what's done is done, the education they received is what they got, and there's only so much that we can do, but figuring out the kinds of reforms that would be necessary to change the K through 12 curriculum so that this just doesn't become an issue for as many students.

#### 11:56:20

REHMDoctor...

#### 11:56:20

VIGDORI think that there are ways that we can do that.

#### 11:56:21

REHMDr. Hacker, I'm gonna give you the last word.

#### 11:56:25

HACKEROkay. All I'm asking, Diane, is that we rethink this requirement that we impose on everyone. Ask ourselves, can we not think of some alternative to algebra?

#### 11:56:42

REHMAndrew Hacker, he's professor emeritus of political science at Queens College of New York. Ed Nolan, program supervisor of mathematics in Montgomery County, Md. Jacob Vigdor, professor of public policy and economics at Duke University. And Judy Bolton-Fasman, she's a blogger and writing on parenting and family life. Thank you all so much. We shall see what happens with algebra. Thanks for listening. I'm Diane Rehm.

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