Impossible Problems – Arising in Education

The is the third in our series of impossible problems articles.  Education is an easy target because so many problems of education have no solution or at least no clear solution consensus. See,
Impossible problems - conflicting information: http://used-ideas.blogspot.com/2013/10/impossible-problems-arising-from.html
Impossible problems - complexity: http://used-ideas.blogspot.com/2013/09/impossible-problems-arising-from.html

Impossible Problems – Arising in Education
by
G. Donald Allen

Almost all of the problems of education are impossible, or at least difficult. In fact, there seems no field of study for which almost every problem is impossible. The education literature is totally loaded with impossible problems; even still we are constantly hearing of local solutions on this problem or that. A teacher has finally connected with her students and this is how… ; A district has developed a professional development program that fully engages the teacher in fully engaging the student…. Yet, none of these solutions generalize or are generalized.

We rarely, if ever, hear of an idea that actually works AND that many or all the schools have adopted it. Reports seem anecdotal. Except one, and that is recently developed and multi-state adoption of the Common Core Curriculum. More on this later. Most general solutions involve only a few premices. (1) If only the teachers would …, and (2) If only the students would … . One could add a third, (3) If only the parents would … . Simply put, many solutions are posited upon the unlikely hope that some fundamental change should occur. Yet, Education, a multi-trillion dollar enterprise, must live within its very own sandbox of exigencies. Parents, students, and teachers are what the human components, and suggesting large changes to any of them is surprisingly difficult.

An analogy I like to use is this: Imagine the Educational enterprise to be a giant oil tanker carrying millions of barrels of oil to some destination. Imagine a new idea or program as a speedboat, buzzing back and forth, to and fro, about the tanker. Eventually it is absorbed; resistance is futile.

Much of this has to do with the apparent failure of our educational system to educate students. There would be none of this conversation if the schools were doing what the public perceives they should be doing. This is proved by the fact that large resources of the colleges are dedicated to various forms of remediation. Students matriculating to colleges can barely write a sentence, cannot do even basic math problems, have massive misconceptions in science, and have very high expectations that seldom involve sustained study.

Complex issues they are, partly owing to the multiplicity of conflicting solutions offered, each with fervent commitment. There is almost no field with more diametrically opposed viewpoints than education. Maybe politics can compete. This causes a level of complexity and conflict unlike most other subjects. This is a vertical and horizontal state of affairs. In educational schools, multiple faculty adhere to this pedagogy or that, and in the general teaching practice the same is true. This, the square-one profession, seems never to have its house in order. Not to savage the participants badly, it must be mentioned that there are few subjects that offer so many conflicting solutions to so many universally agreed upon problems. When equally cogent orthogonal solutions are offered to the same problem this exemplifies the horrific difficulty of the problems, or impossible problems of Education. Moreover, when multiple solutions are offered, they create a sense of confusion.

One fact must be indicated and that is educators are true to themselves, believing each is trying to do the right thing by their students, and believing what they believe is the true course to follow.

For example, in reference only to a simple subject like funding, some suggest more, some less. Some suggest more funding should be awarded to programs, while others suggest a pay increase for teachers. Some suggest there is too much funding for extraneous program having little merit for general educational goals. Before grocery shopping, it is best to make a list of needs, a needs analysis, as it were. Let’s looks at some of the impossible problems Education faces. Each item of our list merits a book length treatment, while we give only a sentence or two.

1. Funding – Tapped out with very high educational taxation, one of the highest in the world, is our current state of schools funding. Is even more funding needed? Yes is the easy answer. “We can do so much more” is the refrain. More faculty, more computer labs, more teacher assistants are just a few items on the needs analysis of educational administrations, together with local and state governments.

2. Teacher quality – Daily missives and epistles issue forth on the quality or lack of quality and expertise of our teachers. Teaching out of field is but one. Licensing exams are too easy, but yet there are dozens of examples of preservice teacher cheating on licensing exams to the point of hiring surrogates to take them. Note that few teachers are asked to teach any course more difficult than courses they took themselves while in the schools. The same may be said at the collegiate level. Yet, there are few voices demanding higher teacher quality at the college level.

3. The status of the teaching profession – Long past are the days of the venerated yet underpaid teacher. The profession is now disrespected far and wide even though many if not most teachers are truly dedicated to their craft. The days have past since a teacher was regarded as a knowledgeable professional dedicated to educating young minds. The teachers was something of a pillar in the community.

4. Student academic performance and standardized testing – That academic low performance in our schools is often blamed on the time required for standardized test preparation is by now standard itself. Teachers claim they don’t like it; schools don’t like it. No one likes it. Everyone does it. Some school systems or teacher organizations have revolted – telling its teachers to ignore the tests. Yet, there is a consistent failure to note that we have the tests only because students were not learning. The tests were a response toward making the schools and teachers more accountable for their performance. So, now the tests are attacked. Right or wrong, if the tests were simply dropped, we’d create them all over again within the decade – and for exactly the same reasons.

5. Racial imbalances and equal educational opportunity – Imbalance is one of the mantras falling under the banner of fairness. In fact, society has not yet learned that some folks take more resources from or of education, and have not yet learned there is a limit to those resources. Education does what it can but cannot turn out Harvard quality graduates in bulk. If there were no racial imbalances, there would be identified imbalances of another flavor. Groups underperforming would be cleverly classified as deprived and calls for more resources toward repairing the imbalance would issue forth. The call for more resources is part and parcel of imbalances – and it works well. So accustomed to these calls is the educational system that they are a significant component of the funding business.

6. Curriculum in relation to labor force needs and global competition – Does the curriculum meet the needs of global competition? This type of question often spawns calls for action, usually by those having no direct classroom connection. These folks want to help, they feel the need, but cannot and will not enter the classroom. They see global competition as something of a technical issue which they address in the only manner available to them – changing the curriculum. If, for example, you see a problem with medical treatment, you may well suggest an increase in the numbers of doctors. You cannot address the issues of the quality of doctors, as this is beyond your knowledge base. What would you do? The only thing you can do! Require stronger licensing standards, that is to say, make more stringent, maybe frequent, qualifying exams? This would put you against the medical establishment, one of those canonical immovable objects in our society.

7. Schools administration – One massive problem with the current state of education rests with the schools administrations. While teachers acclaim their principals to be genuine and caring leaders, the principals must be mindful of the superintendents. Superintendents, on the other hand, are mostly political animals that need to demonstrate achievement of their students. This happens only when the students do well on the standardized tests. This complete the high stakes testing cycle. We also see the rise and reliance on Policy and Procedures (PP) manuals, favoring policy and procedure above local wisdom. This is merely acknowledgment that school officials are perceived to have little of the latter, and to seriously acknowledge that the aggrieved student’s parents may protest any remedy not covered by the despised yet vaunted PP manual. PP thinking has generated those zero-tolerance policies, which select, often unfairly, student-victims for massive punishment for minor violations.

8. Kids hate school – Kids have always hated school. Indeed, schools make or should make students think, and thinking is hard work with no immediate benefit. Yet, in days past most students understood as especially did their parents, that education was one of the keys to a better life. Not just a material life, but an enriched one. But thinking is not fun. It is work! Who will claim that an ignorant person lives a happier, more productive, more enabled life than the one with some learning? Note that “life-long” learning is one of the key mantras of the educational system.

9. Clients and customers - Who are the clients or customers of education? We include the parents, society, and the kids. In this particular question, it appears one’s political views separate who answers what. Surely, we could imagine the students are the customers of the educational product. They study, they learn, they benefit. Yet, also society benefits. Indeed, society needs an educated workforce. The parents are in the middle, representing both camps. They want their kids to be happy in their learning environment, yet want the other kids to learn regardless.

10. Motivation and self-efficacy – This is the latest trend toward improving education. We need to measure motivation and self-efficacy of our students. In that way we can channel into their thinking and develop methods for improvement of the entire enterprise. While there are many positive studies in this direction, it is difficult to make changes on the scales to which we must work. However, it has been shown that self-efficacy is important for student performance, and the only other attribute that may trump this is persistence.

11. Newer problems – As if the above don’t illustrate the impossibility of the Educational system, there are more problems to consider.

a. Teacher shortages, overcrowded and unsafe schools.
b. Unequal access to educational technology
c. Gender bias and the bilingual education debate.
d. Educational enterprise as a social institution.

Examples. While each of the topics above represents impossible problems in their own right and in some cases attempts at solutions, one might believe that’s about it. Yet, there are many more. Indeed, there are dozens more. In the next few paragraphs we look at a few examples of the impossibility of the circumstances modern public Education faces.

Impossible solution. We need better kids. We need better teachers.

Impossible solution. Parents should have confidence in their schools and not meddle in their business. They, the schools, must be regarded as professional organizations, much as an engineering firm is.

Impossible solution. We need a better curriculum. Does anyone actually believe that a few academics dreaming a new curriculum can actually affect radically education? Apparently, about forty states think exactly that.

Impossible problem. Some claim that o improve American education, what is needed is to fix the general social climate. It is not exclusively to focus on the internal school process but to examine and remedy as needed what happens outside of school. Many of the education problems comes from larger social problems such as poor parenting, and limited or ignored social services.

Impossible problem. What is the best pedagogy for teaching math or science? There are two main alternatives, the discovery or constructivist approach to learning wherein the student participates in discovering new knowledge, and the drill and skill approach wherein the student is given the current theory, supposedly internalizes it, practice upon it, and then answers test questions about what is learned. BTW, the terms drill and skill have been convoluted to drill and kill by the constructivists. Yet, let us add that for millennia the drill and skill approach has been used almost exclusively. It allows mediocre teachers to teach and mediocre student to learn – at least something. Even the NCTM (National Council of Teachers of Mathematics), long an advocate of constructivism, has recognized the importance of drill and skill in student education. But the schools of education still strongly advocated constructivism as the tool of modern educational pedagogy.

Impossible Problem. How can high stakes testing be improved? The essence of these tests is toward accountability of teaching and learning. So, we could ask for the improvement of teaching and learning. This is another impossible problems addressed above. Focusing on the testing, we consider two solutions. With the testing format assumed to continue, it would be of some merit to improve the question quality, not to mention accuracy. The accuracy question aside, and this is a different but solvable problem, we take up the format, nominally multiple choice. Detractors of this format claim that multiple choice questions are unreasonable. Learning cannot be accurately measured from such questions. Probably true. But asking students to complete by hand solutions and then to have them graded, also by hand, involves the expenditure of monumental resources, thus making this solution if not possible, but surely impractical. Let’s go to the multiple choice format. Possibly not ideal, this format allows guessing and for this there is a theory of scoring correction already extant – though often not used owing to political constraints. But it is the nature of the distracters that is of some concern. Often, these distracters are loaded with traps. That is, the student proceeding incorrectly upon a solution may find an answer exactly what they have found. They check the box. They get the wrong answer. Why, you may ask, are such distracters entered as an answer choices? The patent answer is that then the teacher can see how students fumble on a given problem. This will inform them of how better to teach. This may sound good, but rarely does the teacher even see the results of these tests, and almost never are they given a report of mis-steps of the students upon answer incorrectly. The information is lost in a muddle of data. So, why the traps? Theory! This is the impossible problem of the impossible problems of high-stakes testing.

Even more. There are more problems.

· How to measure teaching ability? How can we expunge incompetent teachers.

· How can we achieve a larger supply of competent teachers? Federal and state programs abound. Alternatively certified teachers are licensed daily, though they don’t survive in the same numbers are those from teacher preparation colleges.

· Teacher burn-out is rampant. The half-life of teachers is about five years. This is quite a short time given the expense of their education. One solution suggested is early mentoring. It has some positive results, but determining and retaining qualified and effective mentors is a serious if not impossible problem.

· How should administrators interface with teachers? Of course, we know the chapter and verse on this. They should, but exactly how should it be done?

· Teachers are overwhelmingly positive, and tend to interpret all circumstances, at least in surveys and polls, in a positive light. It is their role? We seldom see skepticism about teaching and the merits and the results. I love to give professional development seminars to teachers. They always say good thing, even if I barely showed up.

From the web: http://www.cmu.edu/teaching/solveproblem/step1-problem/

Perennial Problems. As if you haven’t seen a sufficient number of impossible problems of education, there are more. There are websites simply loaded with difficult or impossible problems. On website, in particular, http://www.cmu.edu/teaching/solveproblem/step1-problem/ is devoted to problem solving and offer suggestions to each of the following. The list is long. Some have been covered above. Thankfully, many are perennial and generally acknowledged to be impossible problems.

Attitudes & Motivation. Students…

· Come late to class.
· Lack interest or motivation.
· Performed poorly on an exam.
· Don’t seek help when needed.
· Behave rudely in class.
· Don’t participate in discussion.
· Can't apply what they’ve learned.
· Don't come to lecture.
· Don’t keep up with the reading.

Prerequisite Knowledge, and Preparedness. Students…
· Background knowledge & skills vary widely.
· Group projects aren’t working.
· Can't write.
· Don’t keep up with reading.

Critical Thinking & Applying Knowledge. Students…

• Background knowledge & skills vary widely.
• Don't demonstrate critical thinking.
• Don't know how to do research.
• Can't apply what they’ve learned.

Grading & Assessment. Students…
• Complain the exams are too hard.
• Complain about grades.
• International students feel penalized for their poor language skills.
• Performed poorly on an exam.
• Cheat on assignments and exams.

A Liberation Outlook. There are so many, perhaps too many visions of the roles of education and those of the teacher. In the following, the language is beautiful. The fundamental call is “Can’t we all work together?” Let’s look at this from the philosophy of problem-posing education viewpoint as expostulated by the Brazilian educator Paulo Freire. By some practitioners this is the foundation of modern critical pedagogy. It may be a contradiction, but possibly solving student-teacher contradiction by recognizing that knowledge is not deposited, i.e. transferred, from one (the teacher) to another (the student), but is rather through a dialogue between the two. The argument posited by Freire is that “authentic education is not carried on by “A” for “B” or by “A” about “B,” but rather by “A” with “B.” The representation of knowledge rather than the imposition of it leads to education liberation.

· Which is better? Well that depends on the teacher, particularly on the personality and skill.

· Which is better? That somewhat depends on the particular student receiving the treatment.

The impossible problem for educators is which to choose? Educational experts seem to prefer one to the exclusion of the other, and this has resulted in an impossible conflict between respective camps. As mentioned above, only recently, with the NCTM talking points, have the merits of each approach been endorsed and even coalesced.

Ping-Pong. The endless ping-pong match between students and teachers continues. The impossible question is how much teachers should do to educate their students versus how much should students contribute. It is easy to say that teachers should pull out the stops to communicate and teach. The downside of this prescription is serious burn-out, physically and emotionally. Teachers are regular people with full time jobs and cannot offer their entirety to students on a sustained basis. A teacher has a finite amount to offer. Students must come to class, if not exactly prepared, certainly willing and even eager to learn.

Flipped Out. The flipped classroom is the latest venture for the improved instruction of students. Here the teacher becomes a true facilitator. Students study, usually through videos, lessons prior to the class time. During class the teacher act not as the delivery agent of information but the facilitator to answer questions about the material. In theory, this offers some hope for students. The natural issue obvious to the most casual observer is whether the students will complete their portion of the contract. This is unknown. Actually, aside from a few successful studies, very little is known about the long term efficacy of this new teaching style. However, it has captivated attention in both the schools and colleges and many are rushing into this format. Little research is known. So, the flipped classroom is currently an operational plan based substantially on an intriguing idea and on lots of hope.

Impossible Problems – Arising in Education

by

G. Donald Allen

Almost all of the problems of education are impossible, or at least difficult.  In fact, there seems no field of study for which almost every problem is impossible.  The education literature is totally loaded with impossible problems; even still we are constantly hearing of local solutions on this problem or that.  A teacher has finally connected with her students and this is how… ; A district has developed a professional development program that fully engages the teacher in fully engaging the student….  Yet, none of these solutions generalize or are generalized. 

We rarely, if ever, hear of an idea that actually works AND that many or all the schools have adopted it.  Reports seem anecdotal.   Except one, and that is recently developed and multi-state adoption of the  Common Core Curriculum.  More on this later.   Most general solutions involve only a few premices.  (1) If only the teachers would …, and (2) If only the students would … .  One could add a third, (3) If only the parents would … .  Simply put, many solutions are posited upon the unlikely hope that some fundamental change should occur.  Yet, Education, a multi-trillion dollar enterprise, must live within its very own sandbox of exigencies.  Parents, students, and teachers are what the human components, and suggesting large changes to any of them is surprisingly difficult.

An analogy I like to use is this:  Imagine the Educational enterprise to be a giant oil tanker carrying millions of barrels of oil to some destination.  Imagine a new idea or program as a speedboat, buzzing back and forth, to and fro, about the tanker.  Eventually it is absorbed; resistance is futile.

Much of this has to do with the apparent failure of our educational system to educate students.  There would be none of this conversation if the schools were doing what the public perceives they should be doing. This is proved by the fact that large resources of the colleges are dedicated to various forms of remediation.   Students matriculating to colleges can barely write a sentence, cannot do even basic math problems, have massive misconceptions in science, and have very high expectations that seldom involve sustained study.

 Complex issues they are, partly owing to the multiplicity of conflicting solutions offered, each with fervent commitment.   There is almost no field with more diametrically opposed viewpoints than education.  Maybe politics can compete. This causes a level of complexity and conflict unlike most other subjects.   This is a vertical and horizontal state of affairs.  In educational schools, multiple faculty adhere to this pedagogy or that, and in the general teaching practice the same is true.   This, the square-one profession, seems never to have its house in order.  Not to savage the participants badly, it must be mentioned that there are few subjects that offer so many conflicting solutions to so many universally agreed upon problems.  When equally cogent orthogonal solutions are offered to the same problem this exemplifies the horrific difficulty of the problems, or impossible problems of Education.   Moreover, when multiple solutions are offered, they create a sense of confusion.

One fact must be indicated and that is educators are true to themselves, believing each is trying to do the right thing by their students, and believing what they believe is the true course to follow.

For example, in reference only to a simple subject like funding, some suggest more, some less.  Some suggest more funding should be awarded to programs, while others suggest a pay increase for teachers.  Some suggest there is too much funding for extraneous program having little merit for general educational goals.   Before grocery shopping, it is best to make a list of needs, a needs analysis, as it were.   Let’s looks at some of the impossible problems Education faces.  Each item of our list merits a book length treatment, while we give only a sentence or two.  

1.      Funding – Tapped out with very high educational taxation, one of the highest in the world, is our current state of schools funding.  Is even more funding needed?  Yes is the easy answer.  “We can do so much more” is the refrain. More faculty, more computer labs, more teacher assistants are just a few items on the needs analysis of educational administrations, together with local and state governments.

2.      Teacher quality – Daily missives and epistles issue forth on the quality or lack of quality and expertise of our teachers.  Teaching out of field is but one.  Licensing exams are too easy, but yet there are dozens of examples of preservice teacher cheating on licensing exams to the point of hiring surrogates to take them. Note that few teachers are asked to teach any course more difficult than courses they took themselves while in the schools. The same may be said at the collegiate level.  Yet, there are few voices demanding higher teacher quality at the college level.  

3.      The status of the teaching profession – Long past are the days of the venerated yet underpaid teacher.  The profession is now disrespected far and wide even though many if not most teachers are truly dedicated to their craft.   The days have past since a teacher was regarded as a knowledgeable professional dedicated to educating young minds.  The teachers was something of a pillar in the community.

4.      Student academic performance and standardized testing – That academic low performance in our schools is often blamed on the time required for standardized test preparation is by now standard itself.  Teachers claim they don’t like it; schools don’t like it.  No one likes it.  Everyone does it.  Some school systems or teacher organizations have revolted – telling its teachers to ignore the tests.  Yet, there is a consistent failure to note that we have the tests only because students were not learning.  The tests were a response toward making the schools and teachers more accountable for their performance. So, now the tests are attacked.  Right or wrong, if the tests were simply dropped, we’d create them all over again within the decade – and for exactly the same reasons.

5.      Racial imbalances and equal educational opportunity – Imbalance is one of the mantras falling under the banner of fairness.  In fact, society has not yet learned that some folks take more resources from or of education, and have not yet learned there is a limit to those resources.  Education does what it can but cannot turn out Harvard quality graduates in bulk.   If there were no racial imbalances, there would be identified imbalances of another flavor. Groups underperforming would be cleverly classified as deprived and calls for more resources toward repairing the imbalance would issue forth.  The call for more resources is part and parcel of imbalances – and it works well.  So accustomed to these calls is the educational system that they are a significant component of the funding business. 

6.      Curriculum in relation to labor force needs and global competition – Does the curriculum meet the needs of global competition?  This type of question often spawns calls for action, usually by those having no direct classroom connection.  These folks want to help, they feel the need, but cannot and will not enter the classroom.  They see global competition as something of a technical issue which they address in the only manner available to them – changing the curriculum.  If, for example, you see a problem with medical treatment, you may well suggest an increase in the numbers of doctors.  You cannot address the issues of the quality of doctors, as this is beyond your knowledge base.  What would you do?  The only thing you can do! Require stronger licensing standards, that is to say, make more stringent, maybe frequent, qualifying exams?  This would put you against the medical establishment, one of those canonical immovable objects in our society.  

7.      Schools administration – One massive problem with the current state of education rests with the schools administrations.  While teachers acclaim their principals to be genuine and caring leaders, the principals must be mindful of the superintendents.  Superintendents, on the other hand, are mostly political animals that need to demonstrate achievement of their students.  This happens only when the students do well on the standardized tests.   This complete the high stakes testing cycle.  We also see the rise and reliance on Policy and Procedures (PP) manuals, favoring policy and procedure above local wisdom.  This is merely acknowledgment that school officials are perceived to have little of the latter, and to seriously acknowledge that the aggrieved student’s parents may protest any remedy not covered by the despised yet vaunted PP manual.  PP thinking has generated those zero-tolerance policies, which select, often unfairly, student-victims for massive punishment for minor violations.

8.      Kids hate school – Kids have always hated school.  Indeed, schools make or should make students think, and thinking is hard work with no immediate benefit.  Yet, in days past most students understood as especially did their parents, that education was one of the keys to a better life.  Not just a material life, but an enriched one.  But thinking is not fun.  It is work!  Who will claim that an ignorant person lives a happier, more productive, more enabled life than the one with some learning?  Note that “life-long” learning is one of the key mantras of the educational system.

9.      Clients and customers - Who are the clients or customers of education?  We include the parents, society, and the kids.  In this particular question, it appears one’s political views separate who answers what.  Surely, we could imagine the students are the customers of the educational product.  They study, they learn, they benefit.  Yet, also society benefits.  Indeed, society needs an educated workforce.  The parents are in the middle,  representing both camps.  They want their kids to be happy in their learning environment, yet want the other kids to learn regardless.

10.  Motivation and self-efficacy – This is the latest trend toward improving education.  We need to measure motivation and self-efficacy of our students.  In that way we can channel into their thinking and develop methods for improvement of the entire enterprise.  While there are many positive studies in this direction, it is difficult to make changes on the scales to which we must work.  However, it has been shown that self-efficacy is important for student performance, and the only other attribute that may trump this is persistence.

11.  Newer problems – As if the above don’t illustrate the impossibility of the Educational system, there are more problems to consider.  

a.       Teacher shortages, overcrowded and unsafe schools.

b.      Unequal access to educational technology

c.       Gender bias and the bilingual education debate.

d.      Educational enterprise as a social institution.

Examples. While each of the topics above represents impossible problems in their own right and in some cases attempts at solutions, one might believe that’s about it.  Yet, there are many more.  Indeed, there are dozens more.  In the next few paragraphs we look at a few examples of the impossibility of the circumstances modern public Education faces.

Impossible solution.  We need better kids.  We need better teachers.

Impossible solution.  Parents should have confidence in their schools and not meddle in their business.  They, the schools, must be regarded as professional organizations, much as an engineering firm is.

Impossible solution.  We need a better curriculum. Does anyone actually believe that a few academics dreaming a new curriculum can actually affect radically education?  Apparently, about forty states think exactly that.

Impossible problem.  Some claim that o improve American education, what is needed is to fix the general social climate. It is not exclusively to focus on the internal school process but to examine and remedy as needed what happens outside of school. Many of the education problems comes from larger social problems such as poor parenting, and limited or ignored social services.

Impossible problem.  What is the best pedagogy for teaching math or science?  There are two main alternatives, the discovery or constructivist approach to learning wherein the student participates in discovering new knowledge, and the drill and skill approach wherein the student is given the current theory, supposedly internalizes it, practice upon it, and then answers test questions about what is learned.   BTW, the terms drill and skill have been convoluted to drill and kill by the constructivists.  Yet, let us add that for millennia the drill and skill approach has been used almost exclusively.  It allows mediocre teachers to teach and mediocre student to learn – at least something.  Even the NCTM (National Council of Teachers of Mathematics), long an advocate of constructivism, has recognized the importance of drill and skill in student education.   But the schools of education still strongly advocated constructivism as the tool of modern educational pedagogy. 

Impossible Problem.  How can high stakes testing be improved?   The essence of these tests is toward accountability of teaching and learning.  So, we could ask for the improvement of teaching and learning.  This is another impossible problems addressed above.  Focusing on the testing, we consider two solutions.  With the testing format assumed to continue, it would be of some merit to improve the question quality, not to mention accuracy.  The accuracy question aside, and this is a different but solvable problem, we take up the format, nominally multiple choice.  Detractors of this format claim that multiple choice questions are unreasonable.  Learning cannot be accurately measured from such questions.  Probably true.   But asking students to complete by hand solutions and then to have them graded, also by hand, involves the expenditure of monumental resources, thus making this solution if not possible, but surely impractical.   Let’s go to the multiple choice format.  Possibly not ideal, this format allows guessing and for this there is a theory of scoring correction already extant – though often not used owing to political constraints.  But it is the nature of the distracters that is of some concern.  Often, these distracters are loaded with traps.  That is, the student proceeding incorrectly upon a solution may find an answer exactly what they have found.  They check the box.  They get the wrong answer. Why, you may ask, are such distracters entered as an answer choices?  The patent answer is that then the teacher can see how students fumble on a given problem.  This will inform them of how better to teach.  This may sound good, but rarely does the teacher even see the results of these tests, and almost never are they given a report of mis-steps of the students upon answer incorrectly.  The information is lost in a muddle of data.  So, why the traps?  Theory!  This is the impossible problem of the impossible problems of high-stakes testing.

Even more. There are more problems. 

·         How to measure teaching ability?  How can we expunge incompetent teachers.

·         How can we achieve a larger supply of competent teachers? Federal and state programs abound.  Alternatively certified teachers are licensed daily, though they don’t survive in the same numbers are those from teacher preparation colleges.

·         Teacher burn-out is rampant.  The half-life of teachers is about five years.  This is quite a short time given the expense of their education.  One solution suggested is early mentoring.  It has some positive results, but determining and retaining qualified and effective mentors is a serious if not impossible problem.

·         How should administrators interface with teachers?  Of course, we know the chapter and verse on this.  They should, but exactly how should it be done?

·         Teachers are overwhelmingly positive, and tend to interpret all circumstances, at least in surveys and polls, in a positive light.  It is their role?  We seldom see skepticism about teaching and the merits and the results.   I love to give professional development seminars to teachers.  They always say good thing, even if I barely showed up.

From the web: http://www.cmu.edu/teaching/solveproblem/step1-problem/

Perennial Problems. As if you haven’t seen a sufficient number of impossible problems of education, there are more.  There are websites simply loaded with difficult or impossible problems.  On website, in particular, http://www.cmu.edu/teaching/solveproblem/step1-problem/ is devoted to problem solving and offer suggestions to each of the following.  The list is long.  Some have been covered above. Thankfully, many are perennial and generally acknowledged to be impossible problems. 

Attitudes & Motivation.  Students…

·         Come late to class.

·         Lack interest or motivation.

·         Performed poorly on an exam.

·         Don’t seek help when needed.

·         Behave rudely in class.

·         Don’t participate in discussion.

·         Can't apply what they’ve learned.

·         Don't come to lecture.

·         Don’t keep up with the reading.

Prerequisite Knowledge, and Preparedness. Students…

·         Background knowledge & skills vary widely.

·         Group projects aren’t working.

·         Can't write.

·         Don’t keep up with reading.

Critical Thinking & Applying Knowledge.  Students…

•                     Background knowledge & skills vary widely.

•                     Don't demonstrate critical thinking.

•                     Don't know how to do research.

•                     Can't apply what they’ve learned.

Grading & Assessment.  Students…

•                     Complain the exams are too hard.

•                     Complain about grades.

•                     International students feel penalized for their poor language skills.

•                     Performed poorly on an exam.

•                     Cheat on assignments and exams.

A Liberation Outlook.  There are so many, perhaps too many visions of the roles of education and those of the teacher.  In the following, the language is beautiful.  The fundamental call is “Can’t we all work together?”   Let’s look at this from the philosophy of problem-posing education viewpoint as expostulated by the Brazilian educator Paulo Freire.  By some practitioners this is the foundation of modern critical pedagogy. It may be a contradiction, but possibly solving student-teacher contradiction by recognizing that knowledge is not deposited, i.e. transferred, from one (the teacher) to another (the student),  but is rather  through a dialogue between the two.  The argument posited by Freire is that “authentic education is not carried on by “A” for “B” or by “A” about “B,” but rather by “A” with “B.” The representation of knowledge rather than the imposition of it leads to education liberation.

·         Which is better?  Well that depends on the teacher, particularly on the personality and skill.

·         Which is better?  That somewhat depends on the particular student receiving the treatment.

The impossible problem for educators is which to choose?  Educational experts seem to prefer one to the exclusion of the other, and this has resulted in an impossible conflict between respective camps.  As mentioned above, only recently, with the NCTM talking points, have the merits of each approach been endorsed and even coalesced.

Ping-Pong.  The endless ping-pong match between students and teachers continues.  The impossible question is how much teachers should do to educate their students versus how much should students contribute.  It is easy to say that teachers should pull out the stops to communicate and teach.  The downside of this prescription is serious burn-out, physically and emotionally.  Teachers are regular people with full time jobs and cannot offer their entirety to students on a sustained basis.  A teacher has a finite amount to offer.  Students must come to class, if not exactly prepared, certainly willing and even eager to learn.

Flipped Out.  The flipped classroom is the latest venture for the improved instruction of students.  Here the teacher becomes a true facilitator.  Students study, usually through videos, lessons prior to the class time. During class the teacher act not as the delivery agent of information but the facilitator to answer questions about the material.  In theory, this offers some hope for students.  The natural issue obvious to the most casual observer is whether the students will complete their portion of the contract. This is unknown.  Actually, aside from a few successful studies, very little is known about the long term efficacy of this new teaching style.  However, it has captivated attention in both the schools and colleges and many are rushing into this format.  Little research is known.  So, the flipped classroom is currently an operational plan based substantially on an intriguing idea and on lots of hope.