Good evening welcome to the National Museum of mathematics and to a very special event. I think we are all delighted that the museum is putting on this event tonight and even more delighted that they are doing it with the support of the Mathematical Association of america which is helping out tonight and in particular they loaned us james hansen tonight whom i will introduce in a moment. My name is john ewing. Im the president of math for america and i am a mathematician [applause] this was not meant to be an aa meeting by the way. [laughter] every professional mathematician knows that mathematicians and their subject have a certain reputation. A world famous mathematician is walking in the countryside one day when he comes upon a huge flock of sheep and being a world famous mathematician goes up to the shepherd and makes a proposition. 100 against one of your sheep that i can tell can tell you instantly how many sheep are in the flock. The shepherd knowing that there were an awful lot of sheep said okay, ill try it. The mathematician looks around and said there are 937 sheep in this flock. The shepherd set incredible. Thats incredible. The mathematician picks up an animal, throws around around his shoulder and begins to walk away. The shepherd runs after him, weight, weight he said. Double or nothing i can tell you exactly what your profession is. Now the mathematician thinks this is unlikely so he says sure, go ahead the shipper said, you are a world famous mathematician. Incredible said the mathematician per how could you possibly know . Well said the shepherd, put down my dog and ill tell you. This reputation is not new. In 1914, william lewis, the principle of William Penn High School in philadelphia wrote about democratizing education. He focused on High School Mathematics. My objection he wrote to the traditional requirements is largely empirical. I have seen so many pupils driven out of the school by work which could not have any practical advantage to them and i have watched so many classes under the caption of algebra that i have come to believe that we should discriminate as carefully as possible between those pupils who really need the advance mathematics and those will find other work more profitable. 1914. What mathematics we teach in our high schools has been debated for the past centrally, often for and i am i toward. You may be unaware that arithmetic was not taught in Elementary School in the colonial period. Spelling reading and writing constituted the great them at that time. Arithmetic was known as vulgar. Arithmetic was needed and when it was needed it was learned on the job. By the early 20th century algebra and geometry were part of the curriculum in nearly every high school in the country. The Graduation Rate was 8 as Graduation Rates climb, the role of mathematics became a contentious issue almost everywhere. It was then as it continues to be now the most difficult of subjects for many students did culminated at the end of the 20th century with three provocative and exceptional essays written by underwood dudley, a mathematics professor with the title why math, is mathematics necessary and what is mathematics four. To the dismay of any mathematicians, he argued that there were many good reasons to teach mathematics but utility wasnt one of them. Almost all jobs he wrote require no knowledge of algebra and the llama tree at all. He went on, if algebra were necessary for 75 of all jobs, our algebra, our algebra textbooks would be filled with onthejob problems since examples would be so plentiful. This is clearly not the case. The math mystery by Andrew Hacker is the child of the century long debate. Its also part of woody doug lees essays. The two authors reached very different conclusions. His High School Mathematics, are they serving society. How should be taught and why should be taught . These are are hard questions and i believe that finding answers to hard questions is best done in open forms. Thats why were here tonight. Our two speakers are Andrew Hacker and james. You will be glad to know i have reached the point where i introduce them. Andrew hacker is a professor of Political Science at Queens College in the City University of new york, where in addition to teaching Political Science he has taught an experimental course in mathematics literacy. He was an undergraduate at Amherst College and received his phd from princeton university. He taught at cornell and since then he has been on the faculty of Queens College. He is the author of ten books and a sample of the title suggest their reach. Two nations, blackandwhite, separate, hostile and unequal, mismatch, the growing growing gulf between women and men, higher education, how colleges are wasting our money and failing our kids and what we can do about it. In 19 in 2012 he published an oped entitled is algebra necessary which led to his recent book the math math and other stem delusions. Setting the stage for tonight discussion. Whether or not you agree with the substance of these books im sure you will all agree that the titles are, every one of them exceedingly clever. James grew up in Adelaide Australia and when he speaks tonight you may detect that he is not a native of new york. He received his undergraduate degree in mathematics at Adelaide University and came to the u. S. In 1988 where he received his phd in mathematics also from princeton university. After teaching at st. Marys college in maryland and exceptional liberal arts college, i might add, he followed his wife to boston where he soon turned his attention to the general state of k12 mathematics. Eventually he found himself at a private school in South Borough where he founded the institute of mathematics. He consults with schools all across the globe on the teaching of middle school and High School Mathematics. He is also the author of a number of books, mathematic activities for students in clubs, mathematics galore and worthless puzzle books without words and more without words, both of which im told were being presently translated into serbian. I had offered to complete the translation for him tonight, but he is also the leader of a project based on how we perceive and enjoy mathematics. This will be divided into six segments. 215 minute presentation by each of our speakers to lay out the case, to eight minute responses from each and then questions and answers from the audience while the questions are from the audience and the answers are presumably from the speakers. My job tonight is to keep us on schedule and i will do so with ruthless resolve. I would like professor Heckert Heckert professor hacker to begin the presentation. [applause] thank you. It is a pleasure to be here. I may be the only non mathematician in the house, but i thats the reason im here. At this point it is not my intention to make you all math teachers or to put you out of business. I think youre granting glorious and there are total, at last count because im a statistician, 217,584 teachers of mathematics in this country. I dont get has anything to fear from me. Im a political scientist. The chief duty of clinical scientist is to analyze policy, governmental policies which require everyone to do a certain thing. Very simply if youre going to drive a car you have to pass a test. The government said that. If youre going to have a child, child has to be vaccinated. We understand that. What interested me was governmental policy that we have which is that every single young person in this country will be required to take a full sequence of mathematics. Algebra, geometry, precalc and for many the ideal is to have everybody in calculus. My simple reason for being here and simple reason for writing my book can be summed up in one word. I understand we have some visual aids here. I brought one of my own. May i put it down. [laughter] thank you. And please keep that up while im talking. We currently have, another statistic, 4 million 16yearolds in the goal is to have every single one of them enrolled in algebra two. We have coming up the common core and the common core is, by the way it is for everybody. It says career and College Ready but everybody has to pass the common core test and they are tests which are going to be conducted nationally and algebra two is going to be there. We are going to be in for some problems. We are ready have some. The math requirement, the math heard or if you like takes it tremendous toll every year. We rank, in in the united states, very low, about 28th in the the number of our young people who finish high school. Yes. Our High School Dropout rate is 20 . One out of every five young people you see have failed to finish high school. The major academic reason for that is failure or failing a math class. I know there are other reasons but the academic reason is this. We dont keep exact figures on this but a majority of students eventually fail one or more math classes. Is it because theyre ignorant or stupid or because its because theyre asking something of everyone that we really shouldnt be requiring universally. One out of five doesnt graduate of those who graduate from high school and go on to college 43 do not graduate. Its actually close to 45 . This is one of the highest College Dropout rates in the advanced world. We have more colleges but we have fewer people finishing college. Why because colleges mindlessly require mathematics of everybody , even if youre going to major in poetry or modern dance or interior design. You still have to have an algebra test to get on board. We have a fantastic talent here. Worry are shooting ourselves in the foot. People who would be very skilled and talented in all sorts of fields are not being allowed to proceed or even, at a junior college, somebody who wants an associate degree or certificate in cosmetology, Industrial Design or not that, commercial arts. Even they have to pass a math test and as a result our attrition rate is terrible. 43 of people taking the act are not college or ready. 43 taking it are not College Ready. Do you know why . Its because College Ready requires advanced mathematics for everybody. As a result some very Good Students who might be in my College Class wont be there because of this requirement. Now, my book is called the math math. The more i studied, the more i discovered that people are entrenched, im trying to be kind here, entrenched with a certain occupation, profession or vocation. They will literally say anything to defend the status quo from which they benefit. This can can be true of Police Officers or anyone. I discovered whats being told about math is sheer myth. For example theres a 62 figure, we have something called the american diploma project. 62 of all occupations will need algebra. This is certainly a myth. At most 5 of occupations need algebra. I respect those. In the course of writing my book i went down to marietta georgia where i interviewed aeronautical engineers and i was just blown away how they use calculus to study the ice on wings. There were fantastic things. They certainly need mathematics and wall street who use calculus all the time. They study risks and the rest. But not 62 . Thats a question. If we only talk in occupational terms why the other 95 has to take it. I dont want to get too much into the question that theres a shortage of people with stem qualifications. In fact, the people with degrees in stem subjects, less than half, only slightly more than one third are working in stem occupations now. We actually have an oversupply of people with stem qualifications. We are told we better watch out in the global competition because korea, china, singapore are far ahead of us in mathematics. Its true. Their students score high on the International Math test. They score high because they were 23 hours a day. The biggest illness among young people in korea is sleep deprivation. They were 23 hours a day and i want to say this in the best way. If the International Competitions were on check for crossword puzzles, they would score higher there. The big challenge is not more math but getting our kids to work 23 hours and i dont emphasize that. Theres a whole question of whether or not math sharpens our mind. I agree that studying math and really doing well at it sharpens your mind for dealing with mathematics. Thats for sure. There is no evidence whatever that mastering mathematics makes you excel in other fields. Theres none whatsoever. I did a short test of my own at Queens College because i couldnt find any evidence. I took the math scores of varying coming freshmen and i compared the math scores with the history scores. Weighing evidence, and guess what, the correlation was zero. To be high in math or not in history or vice versa. Map does not help in other fields and its just another myth. Now, there certainly, and im not sure what to call this a myth. There is the view, for example i keep his book by my bedside. Its one of the best books ive read on showing a layperson what mathematics really is. He closes the book, he believes that mathematics is one of the greatest creations of the human mind, perhaps even the greatest. Okay ill go along with that. I simply asked, is it something we created or is it something weve discovered . Newton had to discover it. Its like pie, for example. Waiting create pie but we had to find it and show how to use it. What im saying is, i would really love for everybody to appreciate mathematics. I would love to have math teachers take time and treat it like a liberal art so all of us. [inaudible] theres also the view that mathematics is objective which is to say theres one right answer and you dont have to worry about opinions, bias, things like that. This may well well be true, but theres Something Else going on. Mathematics has builtin biases, not so much the subject but the way we assess it and evaluate it. One thing we know, i have a chapter in the book called gender gap in mathematics. Girls and young women actually get higher grades in math courses than the guys do. They do. We have enough studies across the board to show that. The girls get higher grades. But when it comes to the test men are always ahead. I would really ask you to find some way of having tests because were going to continue to test people to give girls in the young women to show what they know for the last halfcentury girls have been 30 points behind boys on the sat. By the way, thats consequential. One consequence is the National Merit scholarship. The National Merit do not give a gender break down for the winners. They refused to do it. They hide that information. You know why . Because 53 of the people who enter the National Merit competition are girls. Boys end up getting 53 of the awards. Why . Because they score 30 points higher than the girls do on these tests. The same thing thats going to happen with the common core. This is one reason why girls find it harder to get into ivy League Schools. Ivy League Schools require 700 before the open your application on mathematics. Both math and verbal, 700. Two thirds of those 700 are boys. As a result stanford, yale, for example are majority men. Why because of the math requirement. Now girls are doing okay in your classes, but please, i need some advice, the country does on how to help them tests. Math requires okay do i think we should abolish algebra . No. Of course not. I do want to see other options and alternatives and stead of the full sequence for everybody at tenth grade, we can work this out. Begin to offer options i teach a class at my college in the Math Department called numeracy 101 which is about citizen statistics. How to read a corporate report. How to look at the federal budget. It doesnt require any math. I dont think we have to be ashamed of that at all. [applause] and now ill introduce james. Thank you. This is a real honor and a real treat. Thank you doctor hacker. This is a great conversation. It is vital that we reassess the state of Mathematics Education in our nation over and over again. [inaudible] think you for being here today. Its truly wonderful that we adults and parents can double check truths for ourselves and personally assess the claims made in the media and the internet and in general conversation. We are brave enough to ask how do we know what we know and not become. [inaudible] i have enjoyed what he had to say. I have an interpretation that some might find surprising. I think hes arguing strongly for the common core mathematics. [inaudible] there are mighty strong warnings about how not to implement the common core standard. Like me, he doesnt want implementation. [inaudible] above all leading a human discussion experience with mathematics being pushed aside. I couldnt agree more that these are real concerns and many feel the same way. Let me just try putting this on the screen. Im basing my discussion. [inaudible] i just had some beautiful comments about the joy of mathematics. Id like to ask you to share my. [inaudible] about teaching mathematics. I completely agree with dr. Hecker when he proposed in chapter one that we strongly focus on a path when teaching mathematics. He praises philosophy, art, history all white teaching math. We should teach the human story of mathematics. But actually the content of the High School Level can be argued that is somewhat secondary. I have never used a formula in my personal life. Now i view some in my Research Life but learning this formula wasnt the point. I love the human story about how mankind battled for millennia. [inaudible] the success of literally completing a square. While teaching mathematics the High School Teacher has stories to betray with each being a story of symmetry, teaching High High School students of the beauty and power of symmetry. Theyre so much beauty in richness and what theyve been doing right there in that subject. The formula somewhat irrelevant and secondary. To me the goal of education is to help people see and consider and practice taking the road higher thought. It teaches you how to be curious and to learn some great achievements of mankind. Learn how to appreciate art, music and intellectual thought. High school is not about content almost every topic is getting whittled completely away if youre only looking at the utilitarian use of it. When was the last time we had to use a haiku in everyday life. Its all about teaching a safer being an accomplished thinker. I think math is great about teaching problemsolving and thinking through challenges. I think those skills are transferable. Math offers many ranges of human thinking. I think its good at teaching patients and problemsolving and confidence by relying on your wit and battling through challenges. We believe in a common core. [inaudible] its a Human Experience, a Human Experience of context and joy. Now, lets be absolutely clear what the common core actually is so ive gone through, what is the common core . Okay so to standards. Theres content standards. They outline a piece of mathematics that seems to make sense and an appropriate storyline. Theres actually nothing new. Its just people thought very deeply about the storyline that makes sense. I say yay to that. However, the common core goes further. It also says we must have eight statements of thinking. I had to say yes, yes, yes yes yes. Its phenomenal. Its its a major achievement, the common corporate it makes sense of problems. Quantitative. [inaudible] we need to think about what tools are appropriate and necessary mathematics. This one misleads people. Learn how to describe what you really mean what youre talking about. Look for and make structures. You see an equation. Can you step back rather than doing the same calculation over and over again, can you take one step back and solve one general problem instead. They would argue thats the story of algebra right there. Lets be very clear, many people think the common core is hundreds and hundreds of standards. When i said we could each be personally responsible for our matters, you can download the common core standards. I actually counted just 436. Ive counted 436 of these things 149 for high school. 20 of those are optional. Their flexibility. So all is looking good. The biggest point to make is that its not curriculum. Heres the trouble. This is a real danger. It is very easy to confuse state implementation of the common core standards that is that states interpretation of the standards. There are no lesson plans. Its not about lesson plans. There are no uniform tests. There is no scoring system for the nation. And people feel like standards themselves are questions for students. Forgive me. Ill just use examples from the book since its the central theme of the conversation. Use the exponents to interpret equations. How does it give meaning to it . No one applied this and connected it to pascals triangle. They are not questions. They are standards. By the way this one about past quells triangle is optional. The means its optional. Two things to note. None of these standards are optional and theyre not written for student consumption. There were written for experts, the teachers, the curriculum riders. It doesnt mean im going to call it that. Thats the educators choice. The common core is speaking to the academics of the world. It was beautiful. He came up with a lot of words about the common core standards. Forgive me for pulling out some of these and i feel like im being a bit rude here but a lot of this in your book in your book, you did put out a lot of words, i download the document and checked, is it in their . I dont know what that is myself. Its an astronomy word. Many of these terms do not appear in the in there this one is funny. X equation. The word acetone does appear. I do admit its there. Its an optional standard. People are scared of the word algorithm. There is claim that the common core is teaching a lot of these strange algorithms that are related to everyday life. Yes it appears five times. Grades three through six. Its long addition, long subtraction, long while publication, Long Division done. We can check for ourselves are they really part a common core or peoples interpretations interpretation. Its a very scary game whats going on. Ill be fair, there are some terms that are in the common core that people banter about. Elliptical equations, i know thats not my common core. Thats a very big highpowered research but i think it means the word. Ellipsis. You can check these things. Yes there are some scary words that appear in verse functions are in the common five times. That is optional. Interesting. Lets be very clear with the common core is. Not a curriculum, no test, its peoples interpretation that might view it that way. Another thing theyve bantered about and ive seen this in several places is that people worry about statistics. Young people dont understand between correlation and causation. I applaud the common core. They caught this. Its a standard. Please distinguish the difference between correlation and causation. Proofs. This is a scary one. We all have experience from our education days of these two common proofs in geometry. Mathematicians do not do proofs that way. I bet they are a pedagogical device to help students with their thinking. Its a real shocker for many educators, the word simplify does not appear in the common core one place. That is very scary for a lot of teachers. If i ask you to see simplify route 20, ill tell you as a mathematician and looks pretty good. It all depends on what you want to do with it. All these need to reactions. Lets be honest here. This comes up in trigonometry. Its right there on the page. Common core, find just do its in the context. Have a thinking process of doing mathematics. Ill finish off one final example. The idea of literacy. Oh, boy. It is in the common core. So they actually talked about how we need skills in a math curriculum. Again, please check the times of quotes. That was 2003. Many years before the common core was conceived. Look what we do. In number two we want kids to think quantitatively. They are doing spectacular courses. I went through examples. Did i find illustrative math whether trying to find examples related to the core topic dealing with the very issues that his course contents with, yes. I can give you a list of all the examples. Playing with pie. Pie is a big one. We should talk about it at some point. I believe my times up. I will stop there. Thank you. [applause] professor hacker. Okay. Ive been taking some notes during james is talk and alsos comment on them. First of all, im not an expert in a common core and i prefer not to be. I have read all the common core state standards for high school. I went through them and at a certain point i counted Something Like 71764 individual standards. The tests are going to be given next year nationwide, for at least 40 plus states and they are going to be uniform or at lees parallel test. Theyre being done by smarter balance or some test, some states will have their own test but the whole point of the common core was that before the common core each state did it separately. Guess what. In mississippi 90 of the people, High School Seniors were passing in math in mississippi and in minnesota only 74 were. Why because each state had its own test. Common core is going to have a test and you have to, im sorry i shouldnt shake my finger those of us who are math teachers will have to teach to the test. Sorry, you have to because the test results, im not talking about evaluating teachers in terms of salary or even closing schools. Im saying that states themselves will be evaluated on their common core results. It doesnt matter whether we call them standards of curriculum. Just look at whats gonna be on the test that your students will have to go through hour after hour. Okay. And, the failure rate will be disastrous. Why . Because its collegelevel. Almost sat level for the common core. Secondyear algebra for all. We are going to have one or two things. New york and kentucky have already done pilots on common core type tests. Two thirds failed the math in those two test. Next time around we decided we would budge the scoring system so we dont have to thirds failing. Well if we end up with two thirds failing youre going to hear from legislators because of their constituents, zero yes, its going to be white kids from the suburb who fail, not just kids in the back roads of the rural counties. Oh, no. We will see what happens. The question is why . Why are we putting ourselves through this sadistic torture when we really dont have to. Does math help us with problemsolving. Yes with problemsolving in mathematics. Ill give you a problem ive had to deal with five times myself as a citizen i have been a juror in five criminal cases. I might ask why they choose me, well my kind face. Anyway, in each of those trials, five criminals, two murders, the prosecution said we will prove beyond reasonable doubt that the defendant did it. We had to use our minds to solve that problem. Did they have enough proof beyond a reasonable doubt . I assure you that any mathematician in my jury with me were no better than the bicycle messenger, i remember jose pointing something out in my saying to him g jose, i never thought of looking at it that way and jose had never even been in a math class. By the way, rumsfeld number two in the defense department, more than any other person, he gave he gave us the iraq war. I knew him because i knew him up at cornell. He was a math major. His father was a math professor. They have the finest mathematical minds we have. You have a razor sharp mind and they said when we go into baghdad everybody will cheer us in the street and adopt democracy tomorrow. Look, i dont dont even make this fun for Political Science but mathematics shouldnt. The beauty of mathematics and here when james talked about the beauty of mathematics almost a tear rolled down my eye because yes truth is beauty and beauty is truth. What we teach the merchant of venice or jane austens novels, theres, theres a beauty there we can convey. My challenge to Mathematics Teachers and professors is, please, you see a beauty in mathematics. Can you convey that to your students . You have a captive audience. They cant leave. You have a chance to do it. And yet the success rate, im sorry on this, its not good. Only 1 of of bachelor degrees were math majors. It used to be 3 and its down to 1 now. Somethings happening there. Maybe its because the stuff you have to teach in the textbooks that you cant take time off to show sheer duty of pie. Well give it a try. Just one last thing. I have time . Yes. I realize that most of us in this room are academics. Were not vocational teachers. Im a liberal arts teacher. I teach in the liberal arts college but im not training people to be lawyers or things like that. We are really being sold a bill of goods on how we have to train people for stem stem stem. Get them to major in the stem field. Let me put something out because once i heard this i really have to use it also. Go for it. Stem stem stem and even starbucks, look at those coffee machines. That is real high tech stuff. But you know, by the waste starbucks is all over china and russia too. You know its apparent around the world, not the technology, sure but the magic of those words. Who thought up google. Who thought of putting google out there. Putting apple and twitter out there. You dont have to major in math. You dont have to be an engineer. What we do need are not people who are poets. Those are poetic words. Theyre not even going to get college because theyre going to stumble over algebra. Stem may be but just this much, new words like that when you think of the fifth one to put down there that will resound across the globe, i say more power to you. [applause] thank you and now james. Yes the beauty of math the beauty in general. Lets explore all the way through even in Teaching High School algebra two. Testing. Okay we are still on the same page of this culture of testing. Its all about getting what questions, answers to what questions and that seems somewhat joyless to me and i personally would not want to participate. As a High School Teacher i think i was a radical High School Teacher. I used to give quizzes with all the answers supplied. And then a big blank space for students to work on. I said the answer isnt important, its the thinking process behind that. We should have more of that. I used to give these things called hundred packages. You have a month to do this. You just have to keep doing it over and over and over. If it took you a month to figure it out, great. If it took you a week, great. I dont think algebra two is too high a barrier. The issue is how we teach the subject. If we teach with beauty and joy and wonder nest. Mark is going to be somewhere. Lets think of things. Trigonometry is also also deemed scary. Lets talk about a human story. Whats the first thing mankind did when sitting on this earth . Where my . What is this thing . They were sitting on the horizon you might notice the sun rises in the east and it goes overhead for little bit. Then it comes and settles in the west and 12 hours later comes back again, Something Like that, very crude. You probably know its not a perfect circle but its a circle. Thats what the human question would be. Then the question might be how high is it at a certain point. Ive no idea how high it is. The only only thing i can measure is this angle but i can look up at. All i have is the angle of elevation. Maybe its 30 degrees or something. Alright grand grand. Thats the story of trigonometry how do i measure the height of stars at different angles of elevation. Theres a lovely human story here. This was an indian mathematician that called this a jar, assuming you knew what the radius was they called it one big unit, one astronomical unit to the sun. Then math took off in the eight hundreds and it was translated into the arabic. In arabic they tend not to follow the writing of the bowels then math took off and western europe and they went to madrid and translated the map books from arabic into latin. They saw this jb and thought what word is jb so they came up with a new word. Theres the human story of why do you call that the sign of an angle and why that might be the companion to sign. The next question comes from my kids. Okay lets say this is one great big astronomical unit. How high is that star . Okay youve given us a problem. What can i do. Someone might have a problem. It looks like its half an equal letter triangle. In that case what months this length be . At the side of the triangle. It must be half. Suddenly i my kids working on the sine and cosine of 30 degrees just like this. This is joyous. I believe its within reach of everyone and i think theres use of this. I think algebra two is actually within reach of our nation. I do think its anything too deep. I think we clutter the curriculum. Lets decluttering and bring the human story to it. Im all for it. How much time do i have left . 337. 337, truth. Is mathematics helpful with proof this scares me. Proof does come up injury cases and it scares the dickens out of a lot of people. I think we have time for one. Theres a classic example, i think Robin Allen Kaplan wrote about this in the book chances are. Imagine a town where 90 of the the caps are blue and 10 are purple. A crime just took part in an eyewitness said the cab that went away was blue. Ill just do this. You have an eyewitness youre in a town and theres 100 cabs, 90 will be blue and ten will be purple. Is. Is that what i said . All right. So if the eyewitness said i saw purple cab go way, i tested the eyewitness and im being shown the colors blue and purple at random and she was able to identify the correct color 80 of the time. So 80 of the time she is a reliable witness. Shes granted lets lets think about it. Among these 90 blue taxicabs, she will be correct 80 of the time. So 18 cabs she will say theyre actually purple when their blue and 72 will be blue. Of the ten she will say two of them are mistakingly blue and eight of them are actually purple. Okay this witness said she definitely saw a blue cab go away. Shes 80 reliable. What are the chances shes actually correct she said blue of the 72 cases and these two cases down here so i have 34 cases. I want to say at the other way around. Lets say she separable. Its much more convincing. Eight out of 26 times she was actually correct that it was purple. Eight and 26 chance she was within those eight examples. Eight out of 26. That sounds like about 30 for me. Shes only 30 reliable. I believe this thinking does happen in court cases every now and again in the history of this cannot follow this. It would help if i got the numbers right first. [laughter] but that is, i think a good example that in math, 100 hundred of the math we teach is used by somebody and no one individual uses it or ignores 99. 5 of it. However i cant say which part. I think we could reach algebra two as being a reasonable challenge if we teach it with truth, beauty, context, relevance, meaning and joy. Even polynomials are joyful if done in the right way. It really is seeing base ten. Stepping back and finding a joyful picture. Dont teach to the fact if they can divide a polynomial. I dont care about that. Can they talk about them beautifully thank you both. Now its time for questions. you will have a chance to come up and ask individual questions of the speakers. I cant help myself here, i have to make an observation, and the observation is all three of us here are really in some sense james has been a teacher but we are not presently teachers in schools. And schools. We are in some Time University people or University Like people. This is what happens all the time. We are talking about k12 education about mathematics and the role in k12 in high schools and middle schools and Elementary Schools. Can you imagine having a meeting in which we discuss some medical practice and it wasnt a practicing doctor anywhere in sight can you imagine ever doing that, the fact that we are free people all of us who are not teachers says an awful lot about the state of education in this country, and so i would like to say i will take questions from the audience but i would prefer to take questions from k12 teachers if you dont mind. So at least in the beginning i would like to hear from k12 teachers. I will bring the microphone if you could stand up. I teach us to and eighthgrade math [inaudible] what do you suggest you both make great points but we are stuck in the middle. We are the ones stuck in the middle right now. What do you suggest because thats where we are right now. The school, the state, this is something i am freed from and appreciate everything you have to do. This is the politica a politicat just an education question. I want more freedom to teach the beauty of mathematics rather than the standard that you are requiring you to make. I hope they will take that up. My biggest Culture Shock [inaudible] [laughter] my biggest Culture Shock coming from High School Teaching is how busy reflecting on the teaching of High School World has no chance to reflect on teaching. Its really shocking to me and disturbing. I do admit it was exempt from the state standards so im not qualified to teach at the Public School world, but the culture was loud and clear. My experience was do some pushups while youre at it. So nonetheless i got my kids drawing a box on the sit side of their test and still have the questions. Its very hard and costly and you feel like youre alone. Its a very Strong Movement in the examples there is room for it it can be done. I want to speak about a teaching i did here in new york city and Elementary School. I talked problem solving probleo think mathematically and in the weeks before the test, two weeks before the test i said to the teacher you know how to teach them to do a test, now you do that. I want to know what you mean about teaching the test because teaching mathematics is teaching the test. The better the test, the better the students can handle whatever is thrown at them that they might not have seen before. So you are talking about something that i need you to explain because right now its teaching mathematics. Here is my best example. Princeton review and kaplan, you go to them and pay and they teach you how to beat test. In fact some of the people ive talked with say i can teach you to get 400. I know its not great, but 400 without knowing even a thing about mathematics. There could be a test in bulgaria. They teach you how to beat the test. We are professionals, we are teachers. We love learning. My own view is we have to be with the far rightwing on this. Right wing on this. Im against the common core. I would rather have it wouldve totally and leave it to you in the classroom. You are a professional to teach what you think is important and by the way, the french people are teaching Different Things in math classes, fine. A thousand flowers bloom. There isnt one thing everybody has to know. Teaching to the test, that is a scary one because the easy way to interpret that to sing a song to help you memorize it i and tt will solve all the problems. Its kind of what is expected by many parts of the culture. Its all about computation and getting up to speed. The fundamental paradigm shift dont know how to make that happen other than the ways we described earlier but i agree, they thought of the resistance. So theres a lot of what needs to be done. I have an accent that seems to develop some respects so i knew what i was talking about. But believe me i think the phd helped a lot. However, i admit that trust is hard to obtain, i agree. I am a High School Student ive taken common core. And i guess now theres an adjustment period why do we transition to the common core. So the results would be shaky. I think you said only two thirds of students passed it in new york or failed it. So one third. I was wondering if over time do you think as more kids have taken and the teachers have more time to learn how to prep the kids the results will improve and generally it would be more accepted in the common core. Theres a misconception here being proficient. The test has four Different Levels and the misconception is that in order to pass the test, you have to be proficient or advanced, and thats not at all whats meant here. So theres basic, proficient, advanced. The figures you hear about only one third passed it or not correct figures. Thats a misinterpretation of the levels. But now its like somebody answer. They havent failed, they are just not proficient. The word of proficient doesnt mean what you think it means in english. [laughter] lets be very clear. New yorks interpretation of the common core state standards . Who studied in new york . Okay, this was my point earlier. I worried about the implementation of the common core and they know they engaged new york in particular in something very disturbing to me. They said employment in 2015, well start with the curriculum. So every student that has gone through the k9 total experience, and they havent. So i think that its probably going to be a tough challenge to stay in new york if that is the cultural instruction to this. We were told to write advice on this particular curriculum, and i was very nervous. But a 2020 student has already been through the years than a student that hasnt been through it at all. So if we give it a chance, i personally believe theres great hope for it. Testing is always the issue. I worked on the testing again thats going to do anything. But, they are trying to be clever on the test. They are asking why. Heres an algebra problem. Draw a picture of how you might go about. So they are trying to be more in touch with the tests. Im asking a question on behalf of somebody whats supposed the proposal is to abolish standards i would say thats a summary of the proposal. What might be the consequences of that. The consequence of abolishing standard . Whats going to happen with common core, onesizefitsall. Currently, almost half our students dont go on after college come after high school. They just dont go further. Many try college and dont finish. Only about a third finish college. Now what are we going to do for this non academic two thirds . We are going to have the common core standards and the segue into one thing and make them both pass. My answer is if you get rid of it wif we will have much more freedom in tailoring education for various levels of students and i dont mean dumb versus smart. They will be ups drivers. Its an honorable job, but why demand triple of them . [inaudible] the question of publishing the standards. I cant help it. I personally believe that its a beautiful story line. Look at 3,000 years ago. Theres something delightful about those things. Look at the qualification table. You can look at the numbers that generate a whole bunch. It is a basic multiplication table. Thats great for kids to play with. If he lets go of the standards, we let go. Do we want a commonality kids should at least do mathematics and know about the fundamentals, i dont know what that line is. And i guess my argument is i have no trouble with the content of what is deemed algebra two if it is taught in a way that i think it can be. I would say in general standards. One more question. Iam a High School Math teacher and my biggest concern with the idea of not thinking higherlevel math mandatory is that theres already an achievement gap in the country, and my students are already having a lot of doors shut on them and i think i saying okay those that learn math are going to be the ones to learn it. They continue to get the doors closed on them. [applause] that question was asked because it is a basic american question. Back in some trailer park in arkansas or the south bronx or lets say selfproclaimed, but anyway somewhere there is a kid being brought up in the ao ratings like that happen and theres the making of an astrophysicist. Yes, there is such a child. Now the question is how did we discover that child . 100 including the poets and the dancers go into a full mathematics sequence so we find the one person in the trailer park who should be encouraged. Somehow, youve got to work out the probabilities for this. The price that we are paying so that one fraction of 1 will be discovered. Maybe theres a better way to discover a kid at the age of five is a certain life to them, a certain talent. Dont put it on everybody that wants to be a ups driver that needs a High School Diploma for it. What iv eighth. That is the line. If we havwe have people grades n through eight [inaudible] i dont know how to make that call. Lets teach math like you are given the first chapter. Lets reach the young scientists and mathematicians in the audience. I dont think the concept of algebra ii in the standing curriculum are out of reach for the majority of people. I dont think thats just ludicrous to say lets have a go of it. Its the culture of how we do it. We have a culture where teachers can thrive. Ive seen so Many School Districts in some cases get it stuck and we will see you on thursday. Thats not how the human mind works. Maybe thats the issue, dont expect them to be in sync. Thats not the Human Experience. I think its fair enough to have ideas year after year. Lets trust teachers. [applause] than thank you both. Before we close, let me remind you there will be a book table with both speakers on sale over here and you are welcome to ask questions. I would like to close since i already mentioned the final words of his essay is mathematics necessary and it is worth reading because i think in a way it intersects with a vote of the comments that were made by both speakers so he finishes with these words. What do Mathematics Education is for is not for jobs. Its to teach the race to reason. It doesnt always succeed but its the best method that we have. Its not the only road that there is none better. Furthermore it is worth teachi teaching. I would say that mathematics is the most glorious in the human intellect but ive not given into hyperbole so i will not say that. However, when i am before the bar of judgment and asked to justify my life, i will trawl myself up proudly and say i was one of the stewards of mathematics and it came to no harm in my care. I will not say i help people get jobs. Thank you very much. Good night. [applause] [inaudible conversations] next we hear from Political Science professor at Case Western University about his research on competitive elections. I started thinking about competitive elections long ago and i started the project thinking that i was writing as the devils advocate. I saw people assume they are intrinsically good and healthy and i thought it was important to have somebody make the argument in the other direction. So i started the project from the mindset of playing devils advocate and as i kept working on the project, i realized i had an easier time constructing arguments against competitive elections. That can mean a lot of Different Things. It can mean in which there are as many candidates as possible or in which we are uncertain or which there are low barriers to entry. There are a lot of different meanings and one of the problems saying we should have more competitive elections is making them competitive by one definition is making it less competitive guy and others of its important to think about exactly what we mean by terms like competitive. One is the observation that the congressional level very few are competitive by most definitions. Most incumbents win and do so by large margin and if you listen to the political dialogue that is described as a bad thing and there is something wrong in our democracy. However, if we think about it as a decision about whether or not to fire an employee, employees are being retained deterministically on the basis that would suggest that you have a well functioning operation where you see trouble is where you see a company that is regularly firing half of its employees every two years. Thats the sign you have a badly run company. So where it becomes important to understand the distinction is that most than by a large margin. If you think of it as a market then that means that something has gone wrong because it means wwe have that competitive markes monopolies. On the other hand if we think about it as hiring the mechanisms that fact that most are deterministically rehired might mean that everything is working okay. So its important in hiring and firing mechanisms to have a credible threat to fire employees that dont do their job such that they do their job that their employees are retained and that means there are two ways things can go wrong. Firing employees that should have been retained into the other is retaining employees that should have been fired. Either way, you have a problem. If you want to know whether or not there is a problem, we have incumbents that are being systematically rehired on a regular basis. That is a problem if it is the case that the employees should have been fired. So whether or not theres anything wrong is a question of whether the incumbents that are being rehired to shouldnt be rehired. This is where we turn to something we call the paradox. So in observation for one of these very important scholars in Congressional Studies who made the observation that while most americans will say they really dont like congress, if you ask what they think of their own members of congress, they like their own members of congress. So, when we look at the approval or disapproval of congress overall, we are sort of missing the point because if i lived in district number one and you live in district number two, if the opinion is district number two doesnt work for me the only one that works for me is district number one. So, if voters are generally happy with their own members of congress, then that suggests one of two things. Either the voters are being systematically tricked about how well the employees are doing or the system is functioning well. If the system is functioning well we shouldnt worry most are not competitive than we have a bigger problem than the competitive elections and the assessment of whether or not an incumbent deserves to keep the job is a little bit subjective. So its hard to say whether or not they are being systematically tricked. There are limitations on what the voters know. But the times that they are informed of the members of congress is when there is a competitive election usually doing something wrong that means there was a scandal without the incumbent is systematically behaving in ways that constituents dont like and the Campaign Calls attention to it. So the instances that we see the voters best informed about incumbents tend to be the instances in which there is a competitive election and some form of punishment for the income into doing something wrong. If you read the federalist papers, the federalist papers were all about checks and balances and trying to keep anyones faction from getting too much power and trying to keep Public Opinion and the winds of Public Opinion as they shift back and forth from year to year having dramatic changes on the policy. The purpose of the senate was to serve as a check on the house of representatives. The house of representatives was supposed to be essentially the Peoples Chamber and the framers accepted that the house would respond to the whims of the Public Opinion and the goal was to have the senate place a check on that and there was a bias in the system built into the system towards an action based on the premise that no legislation is preferable to bad legislation, and if we look at the political system today, the political system is pretty gridlocked, and the framers wrote the constitution with the objective of creating a bias towards gridlock because it was better than Public Policy shifting to quickly in responses to the whim of the Public Opinion. Theres a lot of variation in the incumbent members of congress and if you think about a group of 435 individuals, any group of the 435 individuals is going to have a range of behavior patterns, a range of knowledge and other factors, and one of the things thats interesting when you look at congress through cspan if you watch the one minute speeches, what you are seeing is the people who choose to give the one minute speeches, and its important to understand that the people who choose to give to the one minute speeches while frequently entertaining are not always the most influential members of congress, and its important to understand a lot of the important work done in congress isnt done on camera. Because some of the important work maneuvering is done in the committee. By the time you get to the floor