The "Experts"
D11 math supervisor Dora Gonzales is a strong believer in constructivist mathematics. She and her closest advisers believe that children have very little need to learn math facts anymore, but are better off developing their own solutions to problems and working in groups with other students to obtain different perspectives, as if the answer to 5X5 has different perspectives. Gonzales pushes a textbook called Everyday Math on elementary schools in the district. This textbook calls for teachers to encourage calculator use in the classroom for students as low as second grade. We are told that due to the technology in existence today, it is more important for students to learn how to use a calculator than it is to learn math tables. Drill and Kill, they call it disparagingly.
The U.S. used to be a world leader in producing graduates who were fluent in math and science. No more. Gonzales claims that we have learned that the brain functions differently than we once thought, so math instruction has had to keep up with the times. Gonzales won't explain how the brain seemed to pick up math skills very well way back when we didn't seem to understand how it worked, and under her new way of teaching, our kids just aren't getting it. The problem goes well beyond Gonzales and D11. She and other D11 administrators have simply fallen for a fad that that has proven to be harmful to math fluency. Fad often takes priority over facts in D11.
Gonzales and her supporters on the school board (which is now everyone) believe that any call for a return to traditional math methods is nothing more than right wing reform madness. Despite the fact that parents are desperate for competent math instruction in the district, Gonzales is determined to hang onto curriculum that is proven to fail kids when they reach high school and beyond.
A Johns Hopkins University math professor named Steve Wilson surveyed fellow math professors around the world on the topic of math. He asked one question in his survey, which was: Do you agree with the following statement? "In order to succeed at freshmen mathematics at my college/university, it is important to have knowledge of and facility with basic arithmetic algorithms, e.g. multiplication, division, fractions, decimals, and algebra, (without having to rely on a calculator)."
Here is what Wilson said about his survey: "I got 93 positive responses and no one disagreed. This is particularly remarkable because if you ask this same bunch what mathematics is, then no two of them will agree. There are at least a couple of dozen who would normally disagree just to be disagreeable...I did not ask for comment but a number of people made powerful compelling statements. I have put them at the end of the list."
Below is the list of professors who replied. Notice the universities at which these professors teach. Knowing what we do about the political makeup of university professors, I imagine that it would be hard to characterize these professors as right-wingers. This is a long read but important to understanding the current math battles. Maybe these people should contact the "experts" in D11 to learn how children's' brains work. Remember, each of the people listed without comment agreed with Wilson's statement.
1. Donald M. Davis Professor of Mathematics Lehigh University 2. Thomas Hunter Associate Professor Swarthmore College Department of Mathematics and Statistics 3. Jim Turner Associate Professor Calvin College 4. Steve Halperin, Dean College of Computer, Mathematical and Physical Sciences University of Maryland, College Park 5. Felix Weinstein Universitaet Bern, Anatomisches Institut 6. Kristine Bauer Assistant Professor Johns Hopkins University 7. Jim Lin Professor of Math University of California at San Diego 8. Clarence Wilkerson Professor Mathematics Department Purdue University 9. Vince Giambalvo Professor of Mathematics University of Connecticut 10. Maria Basterra Assistant Professor University of New Hampshire 11. Frank H. Bria Adjunct Faculty Weber State University 12. Jack Morava Professor of Mathematics The Johns Hopkins University 13. Albert T. Lundell Professor of Mathematics University of Colorado 14. Mark W. Johnson Assistant Professor of Mathematics Syracuse University 15. Jim McClure Professor of Mathematics Purdue University 16. Walter D Neumann Chair of Mathematics Barnard College 17. Robert R. Bruner Professor Wayne State University 18. Ron Umble Professor of Mathematics Millersville University 19. Hessam Tehrani, Assistant Professor Department of Mathemtaics and Computer Science City University of New York 20. David Hurtubise, Ph.D. Assistant Professor of Mathematics Department of Mathematics and Statistics Penn State Altoona 21. Stewart Priddy Professor of Mathematics Northwestern University 22. Tom Goodwillie Professor of Mathematics Brown University 23. Inga Johnson Visiting Assistant Professor University of Rochester 24. Thomas Shimkus Ph.D. Candidate; Lehigh University Mathematics Instructor; DeSales University 25. Ismar Volic Graduate Student Department of Mathematics Brown University 26. John McCleary Department of Mathematics Vassar College 27. Laurence R. Taylor Professor of Mathematics University of Notre Dame 28. Gerd Laures Professor at Bonn University Germany 29. Richard Askey John Bascom Professor of Mathematics University of Wisconsin-Madison 30. Jim Stasheff Professor of Mathematics University of North Carolina - Chapel Hill 31. Hung-Hsi Wu Professor of Mathematics University of California at Berkeley 32. Anthony D. Elmendorf Professor of Mathematics Purdue University Calumet 33. Philip Hirschhorn Professor of Mathematics Chairman, Department of Mathematics Wellesley College 34. Pascal Lambrechts Professor Universit de Louvain-la-Neuve Belgium 35. Carl F. Letsche Assistant Professor Department of Mathematics and Statistics Altoona College Penn State University 36. Hal Sadofsky Associate Professor University of Oregon 37. Ran Levi Senior Lecturer Department of Mathematical sciences University of Aberdeen Scotland, UK 38. Yoram Sagher Professor of Mathematics University of Illinois, Chicago 39. Steve Zelditch, Chair Department of Mathematics Johns Hopkins University 40. W. Stephen Wilson (Chair 1993-96) Professor of Mathematics Johns Hopkins University 41. Ken Monks Professor of Mathematics University of Scranton 42. Norio Iwase Associate Professor Faculty of Mathematics Kyushu University Japan 43. Kevin Iga Assistant Professor, mathematics Pepperdine University 44. William Minicozzi Professor of Mathematics Johns Hopkins University 45. Professor Larry Smith Direktor Mathematisches Institut Universitaet Goettingen Goettingen, Germany 46. Juno Mukai Professor Shinshu University Japan 47. Kathryn Hess Professor Ecole Polytechnique Federale de Lausanne Switzerland 48. John Rognes Professor Department of Mathematics University of Oslo Norway 49. Professor John Greenlees Sheffield University UK 50. Sarah Whitehouse, Dr Universite d'Artois Lens, France 51. Jose L. Rodriguez Assistant Professor University of Almeria Spain 52. John Hunton Reader in Mathematics Department of Mathematics and Computer Science University of Leicester U.K. 53. William Browder (past President of the American Mathematical Society) Professor of Mathematics Princeton University 54. Scott Wolpert Associate Dean for Undergraduate Education College of Computer, Mathematical and Physical Sciences University of Maryland, College Park 55. J. Michael Boardman Professor (Chair 1982-85) Department of Mathematics Johns Hopkins University 56. Ayelet Lindenstrauss Assistant Professor Indiana University 57. Hillel H. Gershenson School of Mathematics University of Minnesota 58. Ralph Cohen Professor of Mathematics Stanford University 59. Dev Sinha Assistant Professor of Mathematics University of Oregon 60. Matthew Ando Assistant Professor Department of Mathematics University of Illinois at Urbana-Champaign 61. Daniel Davis Graduate Student and Teaching Assistant Northwestern University 62. Slava Shokurov Professor of Mathematics Johns Hopkins University 63. Dr. Yuli B. Rudyak Department of Mathematics University of Florida
64. Lowell Abrams Assistant Professor The George Washington University: I am shocked that there is any issue here. I absolutely agree with your statement.
65. Anthony Bahri Professor of Mathematics Rider University Lawrenceville, NJ 08468 - At Rider University we require all students when admitted to have a mastery of basic arithmetic calculation and basic algebra. To ensure this, We administer a placement test for which we do not allow the use of a calculator.
66. Jeanne Duflot Professor Department of Mathematics Colorado State University - However, I should point out that Colorado State University does allow some use of calculators in its introductory calculus courses. I am the course coordinator for third semester calculus (mostly sophomores) and no calculators are permitted to be used on any of my exams, nor on the common final exam for that course. By the way, it's not just your kid's school. Although my children attended a private elementary school at which calculators were not used, as soon as they began attending public school in junior high and high school, calculators appeared.... I must say that sometimes I think they are becoming crippled by too much reliance on calculators. Hopefully they will not entirely forget that they once knew how to do those simple calculations without calculators in elementary school...
67. Randy McCarthy Associate Professor of Mathematics University of Illinois Yes--in fact calculators are often not allowed on exams.
68. Claude Schochet Professor Wayne State University In 1987-91 I served as associate dean of the College of Liberal Arts at Wayne (at the time it consisted of 400 faculty in 23 departments in the humanities, social sciences, and physical sciences.) That it is even slightly in doubt is strong evidence of very distorted curriculum decisions. I do not know even one university-level teacher of mathematics who would disagree with it. I would be truly astonished to meet a person who disagrees.
69. Peter D. Zvengrowski Professor University of Calgary Canada I couldn't agree more. Teaching arithmetic with calculators is like saying we will do physical training by going for 20 km each day, then driving the 20 km in a car daily. I also recall a clever cartoon in a US newspaper about 10 years ago, when George Bush Sr was President. Bush had announced a big initiative in mathematics teaching, to "make the US number 1 in the world by 2000." The cartoon showed two college students reading about Bush's initiative and one remarking to the other "aw what's the difference, it's 7 of one and a half dozen of the other." Clearly whatever Bush had in mind failed, and I'm sure increased use of calculators has been a big part of the problem. Last winter at this time I was visiting Chennai (Madras), and one of my talks was at a Jr H S (called a Secondary School there). I was amazed to see the facility these young students had with arithmetic - of course they never use calculators at all in school.
70. R. James Milgram Professor of Mathematics Stanford University More exactly, what I know is this. Students cannot succeed in any mathematics related course at the university level unless they have completely internalized a real understanding of the number system and the way the basic operations work. It might be argued that we do not really require students to fiercely add, subtract, multiply and divide in our university courses - which is true. But we do require an automatic understanding of these operations and why they work because WE BUILD FROM THERE. It could be that there will be discovered, in time, other ways to give students these prerequisites, but to now, no better or more reliable way has been found than giving them high level arithmetic skills. Unfortunately, programs that in K - 8, substitute calculators for developing these skills have produced students that do not succeed in our university courses. Moreover, in every instance where people responsible for one of these programs have pointed to specific students who have "succeeded" in university courses one of three things has been found when we actually checked. (1) In the majority of cases, what was really said was that the student in question was admitted to the university. When there he or she typically took no mathematics at all (2) The student actually did succeed. However, when we checked with the student he or she explained that his or her parents made sure that tutoring was available to fill in all the gaps. (3) The student's parents had augmented the program, typically with courses from EPGY at Stanford. Some of them had even withdrawn their students from math at their respective schools. Many of these students are currently still of high school age but are taking advanced courses in their local universities. [This last is what I urge that you consider.]
71. Dr. Kathryn Lesh Department of Mathematics Union College Schenectady, NY 12308 In order to succeed at freshmen mathematics at Union College, it is essential to have knowledge of and facility with basic arithmetic algorithms, e.g. multiplication, division, fractions, decimals, and algebra, (without having to rely on a calculator). Students without this ability typically do not make it successfully through their introductory calculus courses, and are often forced to repeat courses or to drop out of engineering/science programs.
72. Martin Tangora Professor University of Illinois, Chicago Here is a new twist. My daughter got a terrible score on her SAT II or whatever, because her calculator's battery was dead, so she borrowed her brother's, but it was set to give exact answers, and she didn't know how to convert them to decimals, and she was too stressed to figure it out, so she couldn't do multiple-choice answers that required knowing whether \pi or e (say) was closer to 3.
73. Professor David Rusin Director of Undergraduate Studies Department of Mathematical Sciences Northern Illinois University Hi Steve, You probably don't remember me but ages ago I was in a Junior Seminar you ran at Princeton. (We worked out of Wallace's "Differential Topology".) I am sorry to see your talent wasted on what I recognize as a battle over mathematical competence. If I can be of help to you, let me know. We have fought with campus groups over the use of calculators in the classroom and over the definition of minimal mathematical competency. In fact, much of our department's response has made it to our web pages in an attempt to cut off these arguments before they are presented to us. Here are the URLs : http://www.math.niu.edu/programs/ugrad/gened.html http://www.math.niu.edu/programs/ugrad/calculators.html http://www.math.niu.edu/programs/ugrad/calc_rationale.html These are directed at university bodies, and may not be applicable to school districts, but they do give a hint of what the _college-bound_ students must prepare for. I have found that it helps a little in these kinds of battles to yield a little when appropriate. As a rule of thumb, we allow the students to use their security blankets in their terminal math courses. So for example the arts and humanities students, who need only one general-purpose math course, get to use calculators at all times. But in exchange we insist on the right to require students to work things out by hand whenever we are preparing them for an additional later math course: the skills learned at one level must be completely internalized before moving on to the next level. (So, for example, our placement test for incoming freshmen is taken WITHOUT calculators.) By this same reasoning, the school districts should insist that all college-bound students be able to show mastery of their subjects with hand calculations. I can give you plenty of ammo if you like: I've already had to prepare responses to many of the most common complaints about our calculator policies, and I've taken the offensive a number of times by trotting out long lists of errors calculators make. One of my favorite attacks is that we are _helping_ the students by insisting that they do things by hand because otherwise they can waste a lot of time when the calculator would fail them. (I regularly ask questions about y = (100-x)^3/10000 or y=40 + log(x) - x/100 when I am forced to allow graphing calculators on tests. Check out what the machines say some time...) Some responses you'll need to prepare for: the NCTM standards call for significant access to technology, and the devaluing of algorithmic calculation; the SAT assumes access to calculators during the exam; and there are studies which claim to show that calculators, _when used appropriately_, enhance student learning. Watch out! No doubt you are aware that the US educational system is releasing increasing numbers of students who fail to meet even the minimal standards imposed by state boards of review. I have had to become well-versed in the matter for several reasons (e.g. we produce many high-school math teachers here). It's a bad situation and I'm glad you're standing up for a minimal competence. You are welcome to quote any of this or our web pages and can quote my titles:
74. H E A Eddy Campbell Associate Dean, Faculty of Arts and Science, Professor of Mathematics and Statistics, Queen's University, Kingston, ON, Canada In order to succeed in our first-year mathematics courses at Queen's University, it is important for students to have a knowledge of and a facility with basic arithmetic algorithms, e.g. multiplication, division, fractions, decimals, and algebra, without having to rely on a calculator. Calculators are not forbidden in our courses, but our experience is clear: if you are relying on them for basic arithmetic you will not be successful. In my experience in this country, Canada, children are still expected to acquire the basic arithmetic skills, and very often my own children come home with strict instructions regarding which questions may be done with the help of a calculator. Calculators are not provided for the junior grades. My own university is proud to say that our students are by objective measures the best in the country, and of the chief joys of teaching them in first-year mathematics courses is their facility with these basic skills. It makes an enormous difference to have students who can add fractions, for example. This last skill is a key indicator of success - if you cannot add fractions, you do not belong in university - we do not have the time nor the resources to teach you that which you should already know on being accepted. If you have graduated from high school without such skills, your high school has cheated you. In my view, the teaching of basic arithmetic skills is not an option for schools, but rather an important part of their mandate. I'd be very unhappy to send my children to a school that thought otherwise.
75. Prof A J Berrick Department of Mathematics National University of Singapore SINGAPORE At my university a stronger statement is true: without such facility noone gets to enter the university!
76. Professor E Farjoun Mathematics Department Hebrew Univ Jerusalem. Israel. This is a very minimal list of knowledge. In fact on top we demand some facility with geometry, trigonometry, and some other subjects. (Editors comment: I had a number of other comments like this but didn't use them.)
77. Timothy Porter Mathematics Division, School of Informatics, University of Wales Bangor United Kingdom In the UK we have had the same type of problem. Finally we have persuaded the Government to include mental arithmetic type operations in the junior school curriculum and to demand calculation without calculators as a necessary skill. It will be years before the harm done is undone (if ever) but there are some hopeful signs. If you need any cross references there is a largish literature (including various international reports) stressing the point you make.
78. Daniel T. Wilshire, Ph.D. Assistant Professor of Mathematics Coordinator / Adjunct Math Faculty Having taught 20 years in public school mathematics and now 16 years at Penn State Altoona in the Mathematics Dept. I heartily agree that public school students must learn the basic arithmetic algorithms to be successful in college mathematics courses. Calculators are a good thing and are being used extensively in my engineering math classes, but successful students know the basics without a calculator.
79. James R. Martino Director of Undergraduate Studies in Mathematics Department of Mathematics Johns Hopkins University We do not use calculators of any kind in any of our courses. As a result, our placement tests for Calculus I and Calculus II require that the students be able to work without a calculator.
80. Jay A. Wood, Chair Department of Mathematics Western Michigan University My department houses mathematics educators as well as mathematicians. While there is much that these two groups disagree about, everyone agrees that all students must have the ability to perform basic "mental mathematics," i.e., perform basic arithmetic operations without the assistance of a calculator.
81. Carl Rupert Penn State Altoona 2001/2 NC Central University 1989 - indefinite After more than a decade of full time college/university level teaching, I agree with the following statement and believe that a failure to understand, and an inability to do simple hand arithmetic, prevents many students from mastering the hand calculation skills necessary for success in college algebra and subsequent higher level classes:
82. Lynn Dover Department of Mathematical and Statistical Sciences University of Alberta I am a candidate for a Ph.D degree in mathematics and a graduate TA (which means that I run tutorial sessions and grade assignments for first and second year mathematics.) RE: your posting to the algebraic topology mailing list. If you can't divide numbers, how on earth are you going to divide polynomials? I could keep coming up with examples all day.
83. William Singer Professor of Mathematics Fordham University I more than agree with your statement about the need for children to learn arithmetic; and the necessity of being able to do simple arithmetic without a calculator. Yes, these skills are necessary to succeed in freshman mathematics at my university. I see many students who, when confronted with an expression like (64)^(-2/3) will hit their calculators to find out the value; but, because they have been raised with the calculator, have no idea what the expression means; how it has been defined; what are the algebraic properties of exponents.
84. Michael Spertus Chairman and Chief Technology Officer Geodesic Systems I am not at a college or university currently, but I am the Chief Technology Officer of a software company. I suppose this may actually count for more than being a university professor with your son's school.
85. Dagmar M. Meyer Research Assistant (PhD) University of Goettingen Germany What a question: the answer is of course "yes, obviously"!!!
86. Hans-Werner Henn Professor of Mathematics Univesite Louis Pasteur Strasbourg, France I completely agree with your statement which is repeated below. It is sad that such things which ought to be completely obvious are controversial! I'd like to add that in my first year courses calculators are usually not authorized in exams. Of course, calculators are (extremely) useful but manipulting them has very little to do with mathematics.
Below are respondents who wrote in after my artificial cutoff. ***********************************************************************
87. Dan Christensen Assistant Professor University of Western Ontario
88. Paul Yiu Professor of Mathematics Florida Atlantic University
89. Norihiko Minami Professor Department of Mathematics Nagoya Institute of Technology I thought it was a joke for you to have asked our opinion about such a self-evident truth, but I am afraid I was wrong. I am very sorry that you had to do this.
90. Younggi Choi Dapartment of Mathematics Education Seoul National University I am surprized at hearing what happened in that school. How can they do not teach math until the middle school? I can not believe it and can not imagine such a situation in Korea. But in these days even in Korea there is some trend of thoughts lowering the standard of math ability. In fact, the eduactional system of America have been giving a great influence on that of Korea. So I am very afraid of that situation. If I were in your place, I would consider seriously having my son transferred to another school in which my son can do math and can make preparation for the future.
91. Martin Bendersky Professor Hunter College City University of New York
92. Jean-Pierre Meyer (Chair 1985-90) Department of Mathematics Johns Hopkins University
93. David C. Johnson Professor of Mathematics University of Kentucky
94. Kojun Abe Professor Department of Mathematical Sciences, Shinshu University, Matsumoto, 390-8621 Japan.
The U.S. used to be a world leader in producing graduates who were fluent in math and science. No more. Gonzales claims that we have learned that the brain functions differently than we once thought, so math instruction has had to keep up with the times. Gonzales won't explain how the brain seemed to pick up math skills very well way back when we didn't seem to understand how it worked, and under her new way of teaching, our kids just aren't getting it. The problem goes well beyond Gonzales and D11. She and other D11 administrators have simply fallen for a fad that that has proven to be harmful to math fluency. Fad often takes priority over facts in D11.
Gonzales and her supporters on the school board (which is now everyone) believe that any call for a return to traditional math methods is nothing more than right wing reform madness. Despite the fact that parents are desperate for competent math instruction in the district, Gonzales is determined to hang onto curriculum that is proven to fail kids when they reach high school and beyond.
A Johns Hopkins University math professor named Steve Wilson surveyed fellow math professors around the world on the topic of math. He asked one question in his survey, which was: Do you agree with the following statement? "In order to succeed at freshmen mathematics at my college/university, it is important to have knowledge of and facility with basic arithmetic algorithms, e.g. multiplication, division, fractions, decimals, and algebra, (without having to rely on a calculator)."
Here is what Wilson said about his survey: "I got 93 positive responses and no one disagreed. This is particularly remarkable because if you ask this same bunch what mathematics is, then no two of them will agree. There are at least a couple of dozen who would normally disagree just to be disagreeable...I did not ask for comment but a number of people made powerful compelling statements. I have put them at the end of the list."
Below is the list of professors who replied. Notice the universities at which these professors teach. Knowing what we do about the political makeup of university professors, I imagine that it would be hard to characterize these professors as right-wingers. This is a long read but important to understanding the current math battles. Maybe these people should contact the "experts" in D11 to learn how children's' brains work. Remember, each of the people listed without comment agreed with Wilson's statement.
1. Donald M. Davis Professor of Mathematics Lehigh University 2. Thomas Hunter Associate Professor Swarthmore College Department of Mathematics and Statistics 3. Jim Turner Associate Professor Calvin College 4. Steve Halperin, Dean College of Computer, Mathematical and Physical Sciences University of Maryland, College Park 5. Felix Weinstein Universitaet Bern, Anatomisches Institut 6. Kristine Bauer Assistant Professor Johns Hopkins University 7. Jim Lin Professor of Math University of California at San Diego 8. Clarence Wilkerson Professor Mathematics Department Purdue University 9. Vince Giambalvo Professor of Mathematics University of Connecticut 10. Maria Basterra Assistant Professor University of New Hampshire 11. Frank H. Bria Adjunct Faculty Weber State University 12. Jack Morava Professor of Mathematics The Johns Hopkins University 13. Albert T. Lundell Professor of Mathematics University of Colorado 14. Mark W. Johnson Assistant Professor of Mathematics Syracuse University 15. Jim McClure Professor of Mathematics Purdue University 16. Walter D Neumann Chair of Mathematics Barnard College 17. Robert R. Bruner Professor Wayne State University 18. Ron Umble Professor of Mathematics Millersville University 19. Hessam Tehrani, Assistant Professor Department of Mathemtaics and Computer Science City University of New York 20. David Hurtubise, Ph.D. Assistant Professor of Mathematics Department of Mathematics and Statistics Penn State Altoona 21. Stewart Priddy Professor of Mathematics Northwestern University 22. Tom Goodwillie Professor of Mathematics Brown University 23. Inga Johnson Visiting Assistant Professor University of Rochester 24. Thomas Shimkus Ph.D. Candidate; Lehigh University Mathematics Instructor; DeSales University 25. Ismar Volic Graduate Student Department of Mathematics Brown University 26. John McCleary Department of Mathematics Vassar College 27. Laurence R. Taylor Professor of Mathematics University of Notre Dame 28. Gerd Laures Professor at Bonn University Germany 29. Richard Askey John Bascom Professor of Mathematics University of Wisconsin-Madison 30. Jim Stasheff Professor of Mathematics University of North Carolina - Chapel Hill 31. Hung-Hsi Wu Professor of Mathematics University of California at Berkeley 32. Anthony D. Elmendorf Professor of Mathematics Purdue University Calumet 33. Philip Hirschhorn Professor of Mathematics Chairman, Department of Mathematics Wellesley College 34. Pascal Lambrechts Professor Universit de Louvain-la-Neuve Belgium 35. Carl F. Letsche Assistant Professor Department of Mathematics and Statistics Altoona College Penn State University 36. Hal Sadofsky Associate Professor University of Oregon 37. Ran Levi Senior Lecturer Department of Mathematical sciences University of Aberdeen Scotland, UK 38. Yoram Sagher Professor of Mathematics University of Illinois, Chicago 39. Steve Zelditch, Chair Department of Mathematics Johns Hopkins University 40. W. Stephen Wilson (Chair 1993-96) Professor of Mathematics Johns Hopkins University 41. Ken Monks Professor of Mathematics University of Scranton 42. Norio Iwase Associate Professor Faculty of Mathematics Kyushu University Japan 43. Kevin Iga Assistant Professor, mathematics Pepperdine University 44. William Minicozzi Professor of Mathematics Johns Hopkins University 45. Professor Larry Smith Direktor Mathematisches Institut Universitaet Goettingen Goettingen, Germany 46. Juno Mukai Professor Shinshu University Japan 47. Kathryn Hess Professor Ecole Polytechnique Federale de Lausanne Switzerland 48. John Rognes Professor Department of Mathematics University of Oslo Norway 49. Professor John Greenlees Sheffield University UK 50. Sarah Whitehouse, Dr Universite d'Artois Lens, France 51. Jose L. Rodriguez Assistant Professor University of Almeria Spain 52. John Hunton Reader in Mathematics Department of Mathematics and Computer Science University of Leicester U.K. 53. William Browder (past President of the American Mathematical Society) Professor of Mathematics Princeton University 54. Scott Wolpert Associate Dean for Undergraduate Education College of Computer, Mathematical and Physical Sciences University of Maryland, College Park 55. J. Michael Boardman Professor (Chair 1982-85) Department of Mathematics Johns Hopkins University 56. Ayelet Lindenstrauss Assistant Professor Indiana University 57. Hillel H. Gershenson School of Mathematics University of Minnesota 58. Ralph Cohen Professor of Mathematics Stanford University 59. Dev Sinha Assistant Professor of Mathematics University of Oregon 60. Matthew Ando Assistant Professor Department of Mathematics University of Illinois at Urbana-Champaign 61. Daniel Davis Graduate Student and Teaching Assistant Northwestern University 62. Slava Shokurov Professor of Mathematics Johns Hopkins University 63. Dr. Yuli B. Rudyak Department of Mathematics University of Florida
64. Lowell Abrams Assistant Professor The George Washington University: I am shocked that there is any issue here. I absolutely agree with your statement.
65. Anthony Bahri Professor of Mathematics Rider University Lawrenceville, NJ 08468 - At Rider University we require all students when admitted to have a mastery of basic arithmetic calculation and basic algebra. To ensure this, We administer a placement test for which we do not allow the use of a calculator.
66. Jeanne Duflot Professor Department of Mathematics Colorado State University - However, I should point out that Colorado State University does allow some use of calculators in its introductory calculus courses. I am the course coordinator for third semester calculus (mostly sophomores) and no calculators are permitted to be used on any of my exams, nor on the common final exam for that course. By the way, it's not just your kid's school. Although my children attended a private elementary school at which calculators were not used, as soon as they began attending public school in junior high and high school, calculators appeared.... I must say that sometimes I think they are becoming crippled by too much reliance on calculators. Hopefully they will not entirely forget that they once knew how to do those simple calculations without calculators in elementary school...
67. Randy McCarthy Associate Professor of Mathematics University of Illinois Yes--in fact calculators are often not allowed on exams.
68. Claude Schochet Professor Wayne State University In 1987-91 I served as associate dean of the College of Liberal Arts at Wayne (at the time it consisted of 400 faculty in 23 departments in the humanities, social sciences, and physical sciences.) That it is even slightly in doubt is strong evidence of very distorted curriculum decisions. I do not know even one university-level teacher of mathematics who would disagree with it. I would be truly astonished to meet a person who disagrees.
69. Peter D. Zvengrowski Professor University of Calgary Canada I couldn't agree more. Teaching arithmetic with calculators is like saying we will do physical training by going for 20 km each day, then driving the 20 km in a car daily. I also recall a clever cartoon in a US newspaper about 10 years ago, when George Bush Sr was President. Bush had announced a big initiative in mathematics teaching, to "make the US number 1 in the world by 2000." The cartoon showed two college students reading about Bush's initiative and one remarking to the other "aw what's the difference, it's 7 of one and a half dozen of the other." Clearly whatever Bush had in mind failed, and I'm sure increased use of calculators has been a big part of the problem. Last winter at this time I was visiting Chennai (Madras), and one of my talks was at a Jr H S (called a Secondary School there). I was amazed to see the facility these young students had with arithmetic - of course they never use calculators at all in school.
70. R. James Milgram Professor of Mathematics Stanford University More exactly, what I know is this. Students cannot succeed in any mathematics related course at the university level unless they have completely internalized a real understanding of the number system and the way the basic operations work. It might be argued that we do not really require students to fiercely add, subtract, multiply and divide in our university courses - which is true. But we do require an automatic understanding of these operations and why they work because WE BUILD FROM THERE. It could be that there will be discovered, in time, other ways to give students these prerequisites, but to now, no better or more reliable way has been found than giving them high level arithmetic skills. Unfortunately, programs that in K - 8, substitute calculators for developing these skills have produced students that do not succeed in our university courses. Moreover, in every instance where people responsible for one of these programs have pointed to specific students who have "succeeded" in university courses one of three things has been found when we actually checked. (1) In the majority of cases, what was really said was that the student in question was admitted to the university. When there he or she typically took no mathematics at all (2) The student actually did succeed. However, when we checked with the student he or she explained that his or her parents made sure that tutoring was available to fill in all the gaps. (3) The student's parents had augmented the program, typically with courses from EPGY at Stanford. Some of them had even withdrawn their students from math at their respective schools. Many of these students are currently still of high school age but are taking advanced courses in their local universities. [This last is what I urge that you consider.]
71. Dr. Kathryn Lesh Department of Mathematics Union College Schenectady, NY 12308 In order to succeed at freshmen mathematics at Union College, it is essential to have knowledge of and facility with basic arithmetic algorithms, e.g. multiplication, division, fractions, decimals, and algebra, (without having to rely on a calculator). Students without this ability typically do not make it successfully through their introductory calculus courses, and are often forced to repeat courses or to drop out of engineering/science programs.
72. Martin Tangora Professor University of Illinois, Chicago Here is a new twist. My daughter got a terrible score on her SAT II or whatever, because her calculator's battery was dead, so she borrowed her brother's, but it was set to give exact answers, and she didn't know how to convert them to decimals, and she was too stressed to figure it out, so she couldn't do multiple-choice answers that required knowing whether \pi or e (say) was closer to 3.
73. Professor David Rusin Director of Undergraduate Studies Department of Mathematical Sciences Northern Illinois University Hi Steve, You probably don't remember me but ages ago I was in a Junior Seminar you ran at Princeton. (We worked out of Wallace's "Differential Topology".) I am sorry to see your talent wasted on what I recognize as a battle over mathematical competence. If I can be of help to you, let me know. We have fought with campus groups over the use of calculators in the classroom and over the definition of minimal mathematical competency. In fact, much of our department's response has made it to our web pages in an attempt to cut off these arguments before they are presented to us. Here are the URLs : http://www.math.niu.edu/programs/ugrad/gened.html http://www.math.niu.edu/programs/ugrad/calculators.html http://www.math.niu.edu/programs/ugrad/calc_rationale.html These are directed at university bodies, and may not be applicable to school districts, but they do give a hint of what the _college-bound_ students must prepare for. I have found that it helps a little in these kinds of battles to yield a little when appropriate. As a rule of thumb, we allow the students to use their security blankets in their terminal math courses. So for example the arts and humanities students, who need only one general-purpose math course, get to use calculators at all times. But in exchange we insist on the right to require students to work things out by hand whenever we are preparing them for an additional later math course: the skills learned at one level must be completely internalized before moving on to the next level. (So, for example, our placement test for incoming freshmen is taken WITHOUT calculators.) By this same reasoning, the school districts should insist that all college-bound students be able to show mastery of their subjects with hand calculations. I can give you plenty of ammo if you like: I've already had to prepare responses to many of the most common complaints about our calculator policies, and I've taken the offensive a number of times by trotting out long lists of errors calculators make. One of my favorite attacks is that we are _helping_ the students by insisting that they do things by hand because otherwise they can waste a lot of time when the calculator would fail them. (I regularly ask questions about y = (100-x)^3/10000 or y=40 + log(x) - x/100 when I am forced to allow graphing calculators on tests. Check out what the machines say some time...) Some responses you'll need to prepare for: the NCTM standards call for significant access to technology, and the devaluing of algorithmic calculation; the SAT assumes access to calculators during the exam; and there are studies which claim to show that calculators, _when used appropriately_, enhance student learning. Watch out! No doubt you are aware that the US educational system is releasing increasing numbers of students who fail to meet even the minimal standards imposed by state boards of review. I have had to become well-versed in the matter for several reasons (e.g. we produce many high-school math teachers here). It's a bad situation and I'm glad you're standing up for a minimal competence. You are welcome to quote any of this or our web pages and can quote my titles:
74. H E A Eddy Campbell Associate Dean, Faculty of Arts and Science, Professor of Mathematics and Statistics, Queen's University, Kingston, ON, Canada In order to succeed in our first-year mathematics courses at Queen's University, it is important for students to have a knowledge of and a facility with basic arithmetic algorithms, e.g. multiplication, division, fractions, decimals, and algebra, without having to rely on a calculator. Calculators are not forbidden in our courses, but our experience is clear: if you are relying on them for basic arithmetic you will not be successful. In my experience in this country, Canada, children are still expected to acquire the basic arithmetic skills, and very often my own children come home with strict instructions regarding which questions may be done with the help of a calculator. Calculators are not provided for the junior grades. My own university is proud to say that our students are by objective measures the best in the country, and of the chief joys of teaching them in first-year mathematics courses is their facility with these basic skills. It makes an enormous difference to have students who can add fractions, for example. This last skill is a key indicator of success - if you cannot add fractions, you do not belong in university - we do not have the time nor the resources to teach you that which you should already know on being accepted. If you have graduated from high school without such skills, your high school has cheated you. In my view, the teaching of basic arithmetic skills is not an option for schools, but rather an important part of their mandate. I'd be very unhappy to send my children to a school that thought otherwise.
75. Prof A J Berrick Department of Mathematics National University of Singapore SINGAPORE At my university a stronger statement is true: without such facility noone gets to enter the university!
76. Professor E Farjoun Mathematics Department Hebrew Univ Jerusalem. Israel. This is a very minimal list of knowledge. In fact on top we demand some facility with geometry, trigonometry, and some other subjects. (Editors comment: I had a number of other comments like this but didn't use them.)
77. Timothy Porter Mathematics Division, School of Informatics, University of Wales Bangor United Kingdom In the UK we have had the same type of problem. Finally we have persuaded the Government to include mental arithmetic type operations in the junior school curriculum and to demand calculation without calculators as a necessary skill. It will be years before the harm done is undone (if ever) but there are some hopeful signs. If you need any cross references there is a largish literature (including various international reports) stressing the point you make.
78. Daniel T. Wilshire, Ph.D. Assistant Professor of Mathematics Coordinator / Adjunct Math Faculty Having taught 20 years in public school mathematics and now 16 years at Penn State Altoona in the Mathematics Dept. I heartily agree that public school students must learn the basic arithmetic algorithms to be successful in college mathematics courses. Calculators are a good thing and are being used extensively in my engineering math classes, but successful students know the basics without a calculator.
79. James R. Martino Director of Undergraduate Studies in Mathematics Department of Mathematics Johns Hopkins University We do not use calculators of any kind in any of our courses. As a result, our placement tests for Calculus I and Calculus II require that the students be able to work without a calculator.
80. Jay A. Wood, Chair Department of Mathematics Western Michigan University My department houses mathematics educators as well as mathematicians. While there is much that these two groups disagree about, everyone agrees that all students must have the ability to perform basic "mental mathematics," i.e., perform basic arithmetic operations without the assistance of a calculator.
81. Carl Rupert Penn State Altoona 2001/2 NC Central University 1989 - indefinite After more than a decade of full time college/university level teaching, I agree with the following statement and believe that a failure to understand, and an inability to do simple hand arithmetic, prevents many students from mastering the hand calculation skills necessary for success in college algebra and subsequent higher level classes:
82. Lynn Dover Department of Mathematical and Statistical Sciences University of Alberta I am a candidate for a Ph.D degree in mathematics and a graduate TA (which means that I run tutorial sessions and grade assignments for first and second year mathematics.) RE: your posting to the algebraic topology mailing list. If you can't divide numbers, how on earth are you going to divide polynomials? I could keep coming up with examples all day.
83. William Singer Professor of Mathematics Fordham University I more than agree with your statement about the need for children to learn arithmetic; and the necessity of being able to do simple arithmetic without a calculator. Yes, these skills are necessary to succeed in freshman mathematics at my university. I see many students who, when confronted with an expression like (64)^(-2/3) will hit their calculators to find out the value; but, because they have been raised with the calculator, have no idea what the expression means; how it has been defined; what are the algebraic properties of exponents.
84. Michael Spertus Chairman and Chief Technology Officer Geodesic Systems I am not at a college or university currently, but I am the Chief Technology Officer of a software company. I suppose this may actually count for more than being a university professor with your son's school.
85. Dagmar M. Meyer Research Assistant (PhD) University of Goettingen Germany What a question: the answer is of course "yes, obviously"!!!
86. Hans-Werner Henn Professor of Mathematics Univesite Louis Pasteur Strasbourg, France I completely agree with your statement which is repeated below. It is sad that such things which ought to be completely obvious are controversial! I'd like to add that in my first year courses calculators are usually not authorized in exams. Of course, calculators are (extremely) useful but manipulting them has very little to do with mathematics.
Below are respondents who wrote in after my artificial cutoff. ***********************************************************************
87. Dan Christensen Assistant Professor University of Western Ontario
88. Paul Yiu Professor of Mathematics Florida Atlantic University
89. Norihiko Minami Professor Department of Mathematics Nagoya Institute of Technology I thought it was a joke for you to have asked our opinion about such a self-evident truth, but I am afraid I was wrong. I am very sorry that you had to do this.
90. Younggi Choi Dapartment of Mathematics Education Seoul National University I am surprized at hearing what happened in that school. How can they do not teach math until the middle school? I can not believe it and can not imagine such a situation in Korea. But in these days even in Korea there is some trend of thoughts lowering the standard of math ability. In fact, the eduactional system of America have been giving a great influence on that of Korea. So I am very afraid of that situation. If I were in your place, I would consider seriously having my son transferred to another school in which my son can do math and can make preparation for the future.
91. Martin Bendersky Professor Hunter College City University of New York
92. Jean-Pierre Meyer (Chair 1985-90) Department of Mathematics Johns Hopkins University
93. David C. Johnson Professor of Mathematics University of Kentucky
94. Kojun Abe Professor Department of Mathematical Sciences, Shinshu University, Matsumoto, 390-8621 Japan.
posted by Craig Cox | 10:31 PM
4 Comments:
This message must gain traction among the parents and general public. The totally corrupt, "we run public education for the benefit of the adults who work there, not the kids," has blinded the inmates of the education fiefdom to the basic truth. The world is an increasingly competitive place. Only those with good foundational skills across the board (including math, science, literacy, etc)have a chance of competing effectively to carve out a good lifestyly for themselves.
The educators who follow such fads because, make no mistake, they put far less pressure on the teachers to really understand the subject, are selfishly harming millions of kids. This is a universal problem across the country. Sure there are degrees of difference in performance (Colorado is among the worst) but those amount to determining who are the best of the poor when it comes to achievement on an international scale.
Everyday Math is a total travesty. For example, it substitues a "new" long division algorithm for the one that has been optimized and refined over millenia. And the algorithm does work for linear numbers. However, the optimized algorithm that is devalued in EM is able to handle division of polynomials while the EM algorithm is not. Thus, EM sets kids up for failure in even moderately complex math.
If you look at the CSAP results in local districts you will see that the % Unsatisfactory in math increases dramatically from the third to tenth grades. This is proof that the math curricula are failing to provide the basics needed to succeed in Middle and High school math. And the constructivist math programs are gaining in popularity and hence the harmful effect they have on our kids.
Time to wake up and smell the coffee, folks, educators are not the experts they pretend to be.
Here is another example of D11 prowess in Math education. Dora was directed by the Superintendent to evaluate all high school algebra teachers this year. CSAP scores indicate that students in 9th and 10th grade are having a difficult time, so, the "experts" have decided to evaluate the algebra teachers instead of the system that produces so many math illiterate K-8 students. In the mean time, the district math curriculum committee is in the process of aligning math curriculum across the high schools, and vertically down to the elementary schools. Can anyone explain why the evaluation is so important, when math curriculum will be changing, perhaps as early as next year? Just what is she doing? Can't she stand up to the Superintendent and suggest that this evaluation is a colossal waste of time? On the other hand, maybe the teacher evaluation is her new job?
Dora has not demonstrated any math prowes whatsoever. Interesting that she is evaluating teachers. As you point out, if students arrive in 9th grade unprepared for math, how is that the fault of 9th and 10th grade teachers.
Interesting that the district is only now "aligning" curriculum. The now "without a job description" Mary Thurman and her side-kick Bev Johnson used to assure me that the hundreds of thousands of dollars shown on the budget for "curriculum alignment" was being well spent. We had high paid people who kept telling us that they were aligning something. Now you're saying that a committee is doing some aligning? It will be interesting to see the curriculum that is adopted. Hopefully it will be something related to math and not some Dora fad.
Craig: To add on regarding Dr. Wilson, here is someone who received all three degrees in math from MIT. Notice I said "math," not math education. Math ed degrees tend to be light on the "math" and heavy on the "education." In addition to working with the U.S. DOE on math issues, Dr. Wilson has also written a paper titled "Elementary School Priorities," which paper highlights why programs like Everyday Math are such failures, in that he talks about all the things that are important for learning math - teaching standard algorithms, having instant recall of basic facts, having a TEXTBOOK with examples - something you won't find with Everyday Math. The paper can be found at http://www.math.jhu.edu/~wsw/papers/PAPERS/ED/ee.pdf. Also, to see a description of what a student prepared for college math looks like, see Dr. Wilson's comments to a group of 130 math teachers, found at: http://www.math.jhu.edu/~wsw/ED/panel If you read these remarks, and if you understand that programs like Everyday Math do not give students those basic tools Dr. Wilson says are so important, you will start to understand why kids in D-11 do so poorly in math the longer they stay in the district - they aren't being taught the skills in elementary school that will allow them to have success in higher level math.
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