Superman is Here!

George D. Poole, PhD

East Tennessee State University

The new movie by Davis Guggenheim, “Waiting for Superman,” is a documentary on American Public Education (APE) decrying its shortcomings and failings.  The title, together with the movie’s story line, suggests this thesis:  APE is in serious trouble!  Who will be the superman-like hero to arrive in the “nick of time” to save our children from the great insufficiencies of APE?  The movie is a bit of a “downer” and in the few cases presented, does not correctly represent the broader spectrum of APE.  However, the film correctly calls for a unified effort by teachers, parents, education leaders, and community, state, and national leaders to work together to become “the superman” APE and our wonderful children so desperately need ([17], [28]).

In another documentary, entitled Race to Nowhere: the Dark side of the American Achievement Culture, Vicki Abeles (mother, director, and education advocate), attempts to represent the “feelings” of America’s students, parents, educators, administrators, and community leaders on the subject of APE.  Abeles uses the very words of many students as they speak against unmanageable schedules, piles of homework, lack of sleep, and mal-nutrition.  In addition, the film provides opportunities for educators to speak on teaching-to-the-standards that apparently allow no room for innovation.  Abeles incorporates into her film candid interviews with students, parents, educators and academicians that leave the viewers wondering how our educational system ended up in its current state ([13]).  Again, as with the first film, the movie challenges all APE stockholders to pick up their beds and walk toward a more right-sized education that prepares America’s youth of “today” for the life that will follow “tomorrow.”   

In response to the United States’ low performances on national and international testing (NAEP, PISA, [6], [22]), and perhaps in response to these two film documentaries, many knowledgeable, passionate, well-meaning education and non-education leaders have offered their thoughts, experiences, wisdom, and monies to fix and improve APE in order to give our kids the “super” education they deserve.  We already spend more money on education per student than any other country in the world ([1], [7], [23]).  Why aren’t we the best at everything:  Reading, writing, science, history, and mathematics?   We know who Bill Gates and Warren Buffet are.  But do we know who Arne Duncan, Ron Clark, Jaime Escalante, Erin Gruwell, and Frieda Reilly are?  Think about it!  Where do our true interests lie relative to APE?

As a consequence of actions by formal groups to improve APE, and on behalf of our nation’s students, we are doing the following:  First, we attempt to address lack of uniformity in student learning expectations through state curriculum standards (usually guided by NCTM standards), and now, nationwide, through the New Common Core Curriculum Standards ([5], [9]).  Second, we attempt to manage quality control in APE through standardized testing at both the state and national level ([7], [9], [10], [27]), but often we keep the results hidden.  Third, as part of education research and development, we operate laboratory schools and build new model schools (called charter schools) to test new paradigms in teaching and curriculum, and new organizational methods through private out-sourcing programs ([12], [22], [27]).  Fourth, we attempt to measure success of our teachers based on their students’ performances on standardized testing along with value-added scores calculated with suspicious math formulas ([3], [7], [10], [15], [26]).   Fifth, we advocate firing teachers who are low performers based Item 4 above, and even less objective criteria ([17], [25]).  Sixth, we believe teacher education programs are weak and shallow, and should be made stronger with more clinical experiences for our aspiring teachers ([3], [6], [19], [26]).  Seventh, we are beginning to make admission requirements into teacher education programs more demanding with greater expectations for aspiring teachers ([3], [5], [8], [14]).  Eighth, we are considering better-pay for better-performing teachers via bonus monies to keep them in the ranks, since half of those teachers entering the work force this fall will be gone in five years ([11], [14]).  Ninth, we provide special financial support (state and federal) to encourage students to become K-12 teachers ([14]).  Tenth, private and federal monies are used to improve teaching and teacher professional development, but certainly not in a uniform consistent way.

Side bar:  I don’t believe it’s the low pay that chases teachers away from APE.  I believe it’s  a) the current level of extraneous burdens imposed on teachers,  b) the cultural-based lack of support and respect for the teaching profession, and c) the weak preparation of teachers by teacher education programs.   Just think about the deplorable attrition rate stated above within the teaching profession!

Quite frankly, we are beating down unmercifully the teachers that we, in teacher education programs across America, are responsible for training and certifying.  If our teachers are not performing at the level they did 50 years ago, I ask you, “Whose fault is that?”  It goes without saying (but I am saying it anyway) we professors in teacher-training programs (TTP) are most responsible for the quality of teachers we certify and license.  Therefore, it is incumbent on all of us in TTP to seek better ways to enlighten, emancipate, and empower aspiring elementary teachers.  In addition, we professors should develop in-service workshops designed to retrain and rekindle the spirits of these low-performing teachers.  Doesn’t that make sense?  Did we professors in TTP properly mentor these aspiring teachers to become the very best at what they do?  Did we warn them that teaching was dynamic, not static, and that both teaching methods and teaching content would change from year-to-year, if not semester-to-semester?  Teaching is not an easy job.  But teachers and teaching is truly America’s gateway to the future.  As Jaime Escalante said it so well, “In the school, the teacher…the teacher is the critical point!”  It always has been, and it always will be!  In APE, the teachers are the linchpin!          

I cannot speak to all levels of teaching.  But here are my thoughts on how to fix the mathematics portion of APE as it relates to K-6 teaching.  With utmost confidence I dare to make this claim:  America’s “superman” is here, and s/he resides in the hearts and minds of teachers all across our great country.  Our problem is not “Waiting for Superman,” nor “Finding Superman!”  Superman is here!  Our problem is that Kryptonite keeps “superman” (our APE teachers) from performing the academic task entrusted to them, namely “teaching our children.”  What is this power-compromising element called Kryptonite?  Where is it found?

Following an epiphany at San Diego State University in the Spring of 2001, under an inspiring “educational evangelist” name Randy Philipp, I turned from being a mathematician with some degree of international renown into a mathematics educator for elementary teachers in Tennessee.  Now, after a decade of humbly trying to figure out why the teaching and learning of K-6 mathematics is so darned hard, I want to share what I have discovered about Kryptonite and its stifling affects on APE, and how the aspiring elementary teachers I teach have learned to avoid Kryptonite in order to become a super teacher in the subject of mathematics.

Kryptonite is composed of this basic substance:  Teacher education programs consisting of shallow K-6 math content, promoting caterpillar-views of K-6 mathematics, and rarely encouraging aspiring young teachers to trust their own thinking skills in mathematics.  Other ingredients of Kryptonite include:  Inadequate in-service teacher support (including minimal funding for classroom supplies and teacher professional travel), nebulous non-productive in-service workshops, standardized student testing, limited or lack of networking among teachers (inter-school and intra-school), insufficient training in technology and its use in teaching and learning, the belief that teaching K-6 math is easy and based on rote procedures, the belief that kids are either naturally good or naturally bad at math, the belief that kids are similar in the ways they think and learn, and finally, the cultural apathy towards education and its professional membership (including parental indifferences and financial support).      

No wonder “superman” (aka super teachers), can only be found in limited places across America.  Kryptonite is everywhere.  But its most critical ingredient is found in elementary education programs (EEP) at institutions of higher learning.   It’s not that mathematics educators, both those in Mathematic Departments and those in Colleges of Education, are collectively doing a bad job of preparing elementary teachers.  They just aren’t “plowing” widely and deeply enough into K-6 mathematics to support full and complete understanding.  Nor are they advocating more time and technology to show teachers how to help themselves and their future students to trust their own thinking skills about mathematics ([26]).  Lipping Ma (Knowing and Teaching Elementary Mathematics: Teachers’ Understanding of Fundamental Mathematics in China & the United States, 1999) encouraged K-6 teachers to acquire a “profound understanding of fundamental mathematics (PUFM).”  Our aspiring teachers need to acquire a level of understanding of K-6 mathematics that supports a butterfly-view, not a caterpillar-view.  I am not talking about calculus and linear algebra!   I am talking about an in-depth study of K-6 mathematics that breeds a full conceptual understanding.  Higher education cannot accomplish this task in 3 or 4 courses that include a methods course.  There needs to be a sequence of 5-7 courses that focuses on the entire content of K-6 mathematics and encourages the PUFM espoused by Ma.  Above all, these courses should be taught by mathematics educators (including those who truly understand K-6 mathematics beyond a superficial, freshmen-level, procedural-view) that can show aspiring elementary teachers how they can trust their own thinking skills over some boring, make-no-sense, procedures that discourage discovery and thwart creative thinking.  K-6 mathematics is NOT about rote, non-thinking processes and procedures.  It is about freedom to think flexibly, resourcefully, and creatively. 

For sure, aspiring teachers will never learn all they need to know about K-6 mathematics from their EEP.  But for these would-be teachers, EEP should accomplish these three things:  First, EEP should enlighten them about K-6 mathematics content that encourages them to trust their own thinking, especially in areas not covered by EEP.  Second, these EEP should emancipate these promising teachers from the belief that mathematics controls them through static, one-way, make-no-sense processes.  Numbers are dead, inanimate objects.  We control numbers and mathematics, not vice versa.  Thanks to Piaget and his notion of “conservation of number,” there are many flexible, make-sense ways to think about numbers and their arithmetic that are far better than rote, one-way, make-no-sense strategies.  Third, EEP should empower these teaching “up-starts” to create interesting, energetic learning environments in which kids can construct make-sense mathematical worlds for themselves.  And not only should we EEP professors prepare pre-service teachers this way, but we should provide in-service teachers with workshops to re-train and extend their professional development to change their teaching paradigms.  Our goal should be to awaken the sleeping giant that resides inside each one of our in-service teachers!  Set them free!  Rejuvenate their spirits!  Raise their level of confidence!  Throw off their Clark Kent attire and become a super teacher ([10], [22]). 

Providing professional assistance to our teachers, who were inadequately trained to begin with, is a far better solution than firing them ([25])!  Removing Kryptonite is a much better solution to improving APE than getting rid of so-called incompetent teachers based on student assessment as promoted by Michelle Rhee, Joel Klein, and other “backward” problem solvers ([25]).   If kids “fall short” in their learning, we don’t fire them or send them home to their parents.  We search for new and different ways to help our kids think about mathematics, thereby helping them to overcome any learning or understanding deficiencies.  This same approach should be true for our aspiring “superman-teachers.”  Our teachers want to be good!   They are receptive to ideas that help them do a better job of teaching.  It is true that there are a few teachers who have dug in their heels and will not change their non-thinking, non-learning, non-interesting, non-teaching, rut-stuck pedagogy methods.  These inept, indifferent teachers should never have been hired to begin with. These very few “misfits” should be fired!  But most of our teachers care about their kids and how much they learn.  They do want to be successful as teachers, and they do NOT want to be responsible for turning kids away from their natural zeal to learn.  But let’s not throw the “kids (teachers) out with the bath water.”  That would be a foolish waste of money that our country has already invested in them ([17], [27]).  On each school district level, let’s follow the pattern of “help” exemplified by Shanghai who matches a high performing school with a lower performing school ([22]).  Administrators and teachers of the higher performing school work closely with the administrators and teachers of the lower performing school until the second school demonstrates similar successes as the first school. 

A Great Math Conspiracy exists about K-6 mathematics.  First, the history of K-6 mathematics predates the history of public education by millennia.  K-6 mathematical content was developed by landowners, merchants, money lenders, tax collectors, builders, and travelers in order to count and measure things for the purpose of comparing and keeping records.  And the strategies that were developed by these “business persons” to add, multiply, subtract, and divide were developed for brevity and space-saving purposes.  These computational “tricks-of-the-trade” were passed down to young apprentices, not to 6 and 7 year-olds.  So contrary to what educators want to tell us, these ole’ timey strategies are neither simple, nor easy to teach.  Moreover, we are not trying to save space on paper, nor on a record-keeping ledger.  Nor are we preparing them to compute at the speed of light!   Give them space and time to engage, explore, explain, and think.  Second, in grades K-6, our teachers in APE should be developing thinking skills among our kids enabling them to solve all the problems they have never seen before, not just copies of previously solved problems using non-thinking problem solving strategies ([10]).  We should promote algebraic thinking, the kind that develops the ability among teachers and students to extrapolate fundamental or key mathematical ideas. 

Prompt, sedentary education is a killer of natural curiosity and thinking skills .  Prompt education is the kind that ask kids to compute 19 + 23 or 73 – 49  ([10]), rather than asking them to “explain the meaning of these abstract symbols and find three different computational strategies to produce the expected result.”  It is the kind of education based on “show and follow” teaching, and where opportunities for students to “engage, explore, discover, and make-sense out of mathematics” are all minimized.  It is the kind of education that is largely promoted in our country…because we (not all, but many) in higher education have not shown our pre-service or in-service teachers how to teach any differently than they were taught in APE.  It is the very reason that Albert Einstein said, “It is a miracle that curiosity can survive public education.”  As reported by Ravitch ([22]), our country does not always prepare the higher performing students, in the more rigorous math content programs, to become elementary teachers.   Teacher education programs are sending out K-6 teachers where, in five years, 50% will have left the profession.  Why is that?  Because we teachers in EEP have not properly screened teaching applicants, and once in, we have not properly prepared them to teach K-6 mathematics.        

Sedentary education is the kind that requires kids to sit at their desks and listen to boring “show and follow” lectures on math, science, history, government, and other subjects.  As did Ron Clark, Erin Gruell, and Frieda Reilly, get kids out of their seats, engaged, exploring, discovering, manipulating, explaining, and making sense out of non-prompt, interesting, realistic math problems.  Well-guided, constructive, collaborative teaching should be the rule of the day in teaching kids to build mathematical worlds that make complete sense, not the exception.  But many teachers are neither prepared nor trained to guide kids in such learning environments.  They are not comfortable enough with their own understanding of K-6 mathematics that would enable them to create open-ended learning environments for their kids.    

Now to the real crux of the matter!  The unattainable goal of NCLB was to make sure all kids were taught by highly qualified teachers.  The more important, attainable goal should have been to make sure all K-6 teachers were taught by highly qualified teacher educators!  Neither the possession of a doctorate, nor experience in teaching in APE guarantees one to be highly qualified to teach content (and possibly pedagogy) of K-6 mathematics to aspiring young teachers.  If that were true, I would have been a highly qualified teacher of K-6 teachers ten years ago. 

Here are the characteristics of super teachers (ST’s = supermen).  ST’s see the big picture of K-6 mathematics.  They possess a butterfly-view of K-6 mathematics, not a caterpillar-view.   They know that the collective, overarching game plan for K-6 teachers is to help their kids learn to count and measure in increasingly faster, more efficient, and more sophisticated ways.  ST’s understand that kids think and learn differently and therefore must be capable of creating different kinds of learning environments to address different learning styles.  They understand Piaget’s notion of disequilibrium.  Consequently, they are comfortable in helping kids accept the notion that learning new concepts can be kind of fuzzy at the beginning.  They understand why “Huh?” moments are just as important to embrace as “Aha!” moments.  ST’s fully understand the power of, and the ability to apply Piaget’s notion of Conservation of Number.  That is, they help their kids understand that they are in full control of numbers, and that they are allowed to modify numbers in arithmetic problems to take advantage of procedures that make more sense than the rote, make-no-sense procedures.  For example, changing      8 x 45 to  8 x (5 x 9) = (8 x 5) x 9 = 40 x 9 = 360 is much easier than standard pencil and paper strategies.  And changing  119 ¸ 7  by breaking up the dividend to obtain the easier division problem  (70 + 28 + 21) ¸ 7 = (70 ¸ 7) + (28 ¸ 7) + (21 ÷ 7) = 10 + 4 + 3 = 17, thereby avoiding traditional, not-so-easy strategies.  And ST’s must be receptive to an unexpected strategy by a student who finds       72 ÷ 8  by  72 ÷ 8 = [(72 + 8) ÷ 8] – 1 = [ 80 ÷ 8 ] – 1 = 10 – 1 = 9.  Or to a student who finds 73 – 29 by adding 1 to each number to obtain  74 – 30 = 44, thereby avoiding “borrowing.”  Moreover, make-sense computational algorithms that students discover on their own are those that stay with them for life, as opposed to those make-no-sense algorithms they are forced to memorize.  ST’s will help their students develop curiosity, and encourage them to trust their own thinking (rather than rely on memory).  In fact, these special teachers will empower their students with back-up plans when, on occasion, memory or recall fails.  For example, for the student who forgets the product  8 x 7 = 56  may fall back on the break apart strategy:   8 x 7 = 8 x (5 + 2) = (8 x 5) + (8 x 2) = 40 + 16 = 56, or other easy to compute equivalents.   

There are a few EEP around the country that are beginning to develop better programs to send out the super teachers whose characteristics are described above.  But for the sake of our kids, we need to move faster.  Within each state, I propose the following:   First, we need to find super math teacher educators who, themselves, possess the characteristics I described above for super teachers.  They must be prepared to lead the crusade, against political and educational resistance, to strengthen EEP by raising entrance standards to teaching, developing stronger math content curricula, and expanding clinical practices that include technology and best teaching practices.  Second, these ST educators must be able to convince other math teacher educators within their state, perhaps with evangelistic passion, that they can work together to become super math teacher educators.  Third, these new ST math educators must develop in-service workshops and summer academies for teachers across their respective states to begin developing ST characteristics among K-6 math teachers.  To significantly improve APE and our students’ performances on state, national, and international testing (NAEP, PISA, [22]), we need to make drastic changes in the places where we can accomplish the most in the quickest way:  We need to strengthen EEP and develop ST math teacher educators.    

References

1.      Jonathan Alter.   A Case of Senioritis: Gates tackles education’s two-headed monster.  Newsweek Magazine.  11/28/2010.

2.      Baker, Barton, Darling-Hammond, Haertel, Ladd, Linn, Ravitch, Rothstein, Shavelson, Shepard.  Problems with the use of student test scores to evaluate teachers.  Economic Policy Institute.  Brief #278.  August 29, 2010.

3.      Stephanie Banchero.  Teacher training is Panned.  Wall Street Journal.  11/16/2010.

4.      Donna Gordon Blankenship.  Economists want to stop teachers’ degree bonuses.  Boston Globe.  11/20/2010.

5.      Carnegie Corporation of New York.  US Teachers Not Well Prepared to Teach Mathematics, Study Finds.  4/15/2010.

6.      Sam Dillon.  Top Test Scores From Shanghai Stun Educators.  New York Times.  12/7/2010.

7.      Sam Dillon.  What Works in the Classroom?  Ask the Students. New York Times.  12/7/2010.

8.      Camille Esch.  Training Better Teachers.   New America Foundation.  11/16/2010.

9.      Sarah Fine.   Moving Forward with the Common Core.  Education Week.  10/20.2010.

10.  Kelly Gallagher.  Why I Will Not Teach to the Test; It’s Time to Focus on Depth Learning, Not Shallow Answers.  Education Week.  11/17/2010.

11.  Claudia Graziano.  School’s Out: Public Education Faces a Crisis in Teacher Retention.   Edutopia.  Feb 2005.  http://www.edutopia.org/new-teacher-burnout-retention  

12.  Frederick M. Hess.  The Same Thing Over and Over.  Education Week.  11/10/1210.

13.  Lisa Johnson.  School Today is a Race to Nowhere.  Technorati.  9/4/2010.

14.  Kevin Kiley.   Teacher Training Should Be More Practical and Measured Better, Report Says.  Chronicle of Higher Education.  11/16/2010.

15.  Mitchell Landsberg.  Influence of Teachers Unions in Question.  Los Angeles Times.  11/7/2010.

16.  Los Angeles Times Editorial.  The “highly qualified” gap.  11/26/2010.

17.  David Liebowitz.  ‘Superman’ and Solidarity:  Colliding Views of Education’s Future.  Education Week.   10/20/2010.

18.  Dennis Littky.  Big Picture Learning.  Who wants a standardized kid, anyway?

19.  National Council on Teacher Quality.  A Review of Illinois Teacher Preparation.  Executive Summary.   http://www.nctq.org/edschoolreports/illinois/

20.  John Norton. Teachers Wonder:  How Much More Can We Take?  Teacher Magazine.  12/1/2010.

21.  Jim Olsen.  Illinois Educator Preparation Groups Respond to New Ratings Report (on Illinois). Western Illinois University website:  http://www.wiu.edu/coehs/ilEducator.php

22.  Diane Ravitch.   The Real Lessons of PISA.   Education Week.   12/14/2010.

23.  Anthony Rebora.   Gates, Ravitch, Seniority Pay and Lawn Mowers.  Teacher Magazine.  11/30/2010.

24.  Jesse Rothstein.  Review of Learning About Teaching (by Bill and Melinda Gates).  National Education Policy Center, Boulder, CO.  January 13, 2011.

25.  Richard Rothstein.  How to Fix Our Schools.  Economic Policy Institute.  Brief #286. 10/14/2010.

26.  Bonnie M. Rubin and Tara Malone.  Many Illinois Colleges Don’t Prepare Teachers for the Classroom.  Chicago Tribune.  11/9/2010.

27.  Paul Tough.  What I have learned about great teachers.  Parade Magazine.  Oct. 24, 2010.

Assessing American Public Education by Evaluating Our Teachers!

How Hard is That?

American Public Education (APE) is important to all of us.  Virtually all persons who contribute to our health, wealth, freedom, and happiness in America emerged from APE.  But APE is an extremely complex, not-so-well organized, and insufficiently funded enterprise that attempts to educate “all” of our children between ages 5 and 19.  And these children are all as different as snowflakes from a blizzard.  It is a wondrous achievement that APE is as successful as it is.

The linchpin in APE is our underpaid and overworked teachers!  Please don’t blame parents, poverty, ethnicity, religion, and unconcerned school administrators!  Ron Clark, Erin Gruell, Frieda Reilly, and Jaime Escalante didn’t!  And they succeeded as teachers despite a multitude of student differences, student backgrounds, and apathetic school leaders! According to Jaime Escalante, “In the school, the teacher … the teacher is the critical point.”  Amen!  

But trying to assess APE according to how well teachers educate our children is kind of like trying to assess all of the parents in the United States on how well they are “raising” their children.  How hard is that?  Consider this:  Each teacher has a nine-month window of opportunity to help a child learn.  But the child’s education spans 12 to 13 years, impacted by a dozen or more teachers.  Educating a child is a collective enterprise by many different teachers. When is the best time to assess how well a teacher impacts the life of a child with respect to a subject, say mathematics, and how should it be done?  This is an extremely complex undertaking.

I strongly believe that state and federal monies spent on education would be better spent in providing stronger teacher education programs (who certify and license teachers, and therefore are the most responsible for teacher weaknesses and deficiencies) and stronger professional development programs (worthwhile in-service workshops that are grade-band sensitive) than trying to assess teaching.  Evaluating teachers fairly and accurately is intractable, if not impossible, and proves absolutely nothing.  Value-added assessments are a prime example.  From a mathematician turned mathematics teacher educator.  George Poole, Ph.D. East Tennessee State University.

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