The Unreasonable E?ectiveness of Mathematics in the Natural Sciences
by Eugene Wigner1
“Mathematics,rightly viewed,possesses not only truth,but supreme beauty,a
beauty cold and austere,like that of sculpture,without appeal to any part of our
weaker nature,without the gorgeous trappings of painting or music,yet sublimely
pure,and capable of a stern perfection such as only the greatest art can show.The
true spirit of delight,the exaltation,the sense of being more than Man,which is the
touchstone of the highest excellence,is to be found in mathematics as surely as in
poetry.”
Bertrand Russell,Study of Mathematics There is a story about two friends,who were classmates in high school,talking about their jobs.One of them became a statistician and was working on population trends.He showed a reprint to his former classmate.The reprint started,as usual,with the Gaussian distribution and the statistician explained to his former classmate the meaning of the symbols for the actual population,for the average population,and so on.His classmate was a bit incredulous and was not quite sure whether the statistician was pulling his leg.“How can you know that?”was his query.“And what is this symbol here?”“Oh,”said the statistician,“this is pi.”“What is that?”“The ratio of the circumference of the circle to its diameter.”“Well,now you are pushing your joke too far,”said the classmate,“surely the population has nothing to do with the circumference of the circle.”Naturally,we are inclined to smile about the simplicity of the classmate’s approach.Nevertheless,when I heard this story,I had to admit to an eerie feeling because,surely,the reaction of the classmate betrayed only plain common sense.I was even more confused when,not many days later,someone came to me and expressed his bewilderment2with the fact that we make a rather narrow selection when choosing the data on which we test our theories.“How do we know that,if we made a theory which focuses its attention on phenomena we disregard and disregards some of the phenomena now commanding our attention,that we could not build another theory which has little in common with the present one but which,nevertheless,explains just as many phenomena as the present theory?”It has to be admitted that we have no de?nite evidence that there is no such theory.
The preceding two stories illustrate the two main points which are the subjects of the present discourse.The?rst point is that mathematical concepts turn up in entirely unexpected con-nections.Moreover,they often permit an unexpectedly close and accurate description of the phenomena in these connections.Secondly,just because of this circumstance,and because we do not understand the reasons of their usefulness,we cannot know whether a theory formulated in terms of mathematical concepts is uniquely appropriate.We are in a position similar to that of a man who was provided with a bunch of keys and who,having to open several doors in suc-cession,always hit on the right key on the?rst or second trial.He became skeptical concerning the uniqueness of the coordination between keys and doors.
Most of what will be said on these questions will not be new;it has probably occurred to most scientists in one form or another.My principal aim is to illuminate it from several sides.The ?rst point is that the enormous usefulness of mathematics in the natural sciences is something bordering on the mysterious and that there is no rational explanation for it.Second,it is just this uncanny usefulness of mathematical concepts that raises the question of the uniqueness of our 1Eugene Wigner,“The Unreasonable E?ectiveness of Mathematics in the Natural Sciences,”in Communica-tions in Pure and Applied Mathematics,vol.13,No.I(February1960).New York:John Wiley&Sons,Inc. Copyright1960by John Wiley&Sons,Inc.
2The remark to be quoted was made by F.Werner when he was a student in Princeton.
physical theories.In order to establish the?rst point,that mathematics plays an unreasonably important role in physics,it will be useful to say a few words on the question,“What is mathematics?”,then,“What is physics?”,then,how mathematics enters physical theories,and last,why the success of mathematics in its role in physics appears so ba?ing.Much less will be said on the second point:the uniqueness of the theories of physics.A proper answer to this question would require elaborate experimental and theoretical work which has not been undertaken to date.
What is Mathematics?
Somebody once said that philosophy is the misuse of a terminology which was invented just for this purpose.3In the same vein,I would say that mathematics is the science of skillful operations with concepts and rules invented just for this purpose.The principal emphasis is on the invention of concepts.Mathematics would soon run out of interesting theorems if these had to be formulated in terms of the concepts which already appear in the axioms.Furthermore, whereas it is unquestionably true that the concepts of elementary mathematics and particularly elementary geometry were formulated to describe entities which are directly suggested by the actual world,the same does not seem to be true of the more advanced concepts,in particular the concepts which play such an important role in physics.Thus,the rules for operations with pairs of numbers are obviously designed to give the same results as the operations with fractions which we?rst learned without reference to“pairs of numbers.”The rules for the operations with sequences,that is,with irrational numbers,still belong to the category of rules which were determined so as to reproduce rules for the operations with quantities which were already known to us.Most more advanced mathematical concepts,such as complex numbers, algebras,linear operators,Borel sets,and this list could be continued almost inde?nitely,were so devised that they are apt subjects on which the mathematician can demonstrate his ingenuity and sense of formal beauty.In fact,the de?nition of these concepts,with a realization that interesting and ingenious considerations could be applied to them,is the?rst demonstration of the ingeniousness of the mathematician who de?nes them.The depth of thought which goes into the formulation of the mathematical concepts is later justi?ed by the skill with which these concepts are used.The great mathematician fully,almost ruthlessly,exploits the domain of permissible reasoning and skirts the impermissible.That his recklessness does not lead him into a morass of contradictions is a miracle in itself:certainly it is hard to believe that our reasoning power was brought,by Darwin’s process of natural selection,to the perfection which it seems to possess.However,this is not our present subject.The principal point which will have to be recalled later is that the mathematician could formulate only a handful of interesting theorems without de?ning concepts beyond those contained in the axioms and that the concepts outside those contained in the axioms are de?ned with a view of permitting ingenious logical operations which appeal to our aesthetic sense both as operations and also in their results of great generality and simplicity.4The complex numbers provide a particularly striking example for the foregoing. Certainly,nothing in our experience suggests the introduction of these quantities.Indeed,if a mathematician is asked to justify his interest in complex numbers,he will point,with some indignation,to the many beautiful theorems in the theory of equations,of power series,and of analytic functions in general,which owe their origin to the introduction of complex numbers. The mathematician is not willing to give up his interest in these most beautiful accomplishments 3This statement is quoted here from W.Dubislav’s Die Philosophie der Mathematik in der Gegenwart(Berlin: Junker and Dunnhaupt Verlag,1932),p.1.
4M.Polanyi,in his Personal Knowledge(Chicago:University of Chicago Press,1958),says:“All these di?culties are but consequences of our refusal to see that mathematics cannot be de?ned without acknowledging its most obvious feature:namely,that it is interesting”(p188).
of his genius.5
What is Physics?
The physicist is interested in discovering the laws of inanimate nature.In order to understand this statement,it is necessary to analyze the concept,“law of nature.”The world around us is of ba?ing complexity and the most obvious fact about it is that we cannot predict the future. Although the joke attributes only to the optimist the view that the future is uncertain,the optimist is right in this case:the future is unpredictable.It is,as Schrodinger has remarked,a miracle that in spite of the ba?ing complexity of the world,certain regularities in the events could be discovered.One such regularity,discovered by Galileo,is that two rocks,dropped at the same time from the same height,reach the ground at the same time.The laws of nature are concerned with such regularities.Galileo’s regularity is a prototype of a large class of regularities.It is a surprising regularity for three reasons.
The?rst reason that it is surprising is that it is true not only in Pisa,and in Galileo’s time, it is true everywhere on the Earth,was always true,and will always be true.This property of the regularity is a recognized invariance property and,as I had occasion to point out some time ago,without invariance principles similar to those implied in the preceding generalization of Galileo’s observation,physics would not be possible.The second surprising feature is that the regularity which we are discussing is independent of so many conditions which could have an e?ect on it.It is valid no matter whether it rains or not,whether the experiment is carried out in a room or from the Leaning Tower,no matter whether the person who drops the rocks is a man or a woman.It is valid even if the two rocks are dropped,simultaneously and from the same height,by two di?erent people.There are,obviously,innumerable other conditions which are all immaterial from the point of view of the validity of Galileo’s regularity.The irrelevancy of so many circumstances which could play a role in the phenomenon observed has also been called an invariance.However,this invariance is of a di?erent character from the preceding one since it cannot be formulated as a general principle.The exploration of the conditions which do,and which do not,in?uence a phenomenon is part of the early experimental exploration of a?eld.It is the skill and ingenuity of the experimenter which show him phenomena which depend on a relatively narrow set of relatively easily realizable and reproducible conditions.6 In the present case,Galileo’s restriction of his observations to relatively heavy bodies was the most important step in this regard.Again,it is true that if there were no phenomena which are independent of all but a manageably small set of conditions,physics would be impossible. The preceding two points,though highly signi?cant from the point of view of the philosopher, are not the ones which surprised Galileo most,nor do they contain a speci?c law of nature.The law of nature is contained in the statement that the length of time which it takes for a heavy object to fall from a given height is independent of the size,material,and shape of the body which drops.In the framework of Newton’s second“law,”this amounts to the statement that the gravitational force which acts on the falling body is proportional to its mass but independent of the size,material,and shape of the body which falls.
The preceding discussion is intended to remind us,?rst,that it is not at all natural that“laws of nature”exist,much less that man is able to discover them.7The present writer had occasion, 5The reader may be interested,in this connection,in Hilbert’s rather testy remarks about intuitionism which “seeks to break up and to dis?gure mathematics,”Abh.Math.Sem.,Univ.Hamburg,157(1922),or Gesammelte Werke(Berlin:Springer,1935),p.188.
6See,in this connection,the graphic essay of M.Deutsch,Daedalus87,86(1958).A.Shimony has called my attention to a similar passage in C.S.Peirce’s Essays in the Philosophy of Science(New York:The Liberal Arts Press,1957),p.237.
7E.Schrodinger,in his What Is Life?(Cambridge:Cambridge University Press,1945),p.31,says that this second miracle may well be beyond human understanding.
some time ago,to call attention to the succession of layers of“laws of nature,”each layer containing more general and more encompassing laws than the previous one and its discovery constituting a deeper penetration into the structure of the universe than the layers recognized before.However,the point which is most signi?cant in the present context is that all these laws of nature contain,in even their remotest consequences,only a small part of our knowledge of the inanimate world.All the laws of nature are conditional statements which permit a prediction of some future events on the basis of the knowledge of the present,except that some aspects of the present state of the world,in practice the overwhelming majority of the determinants of the present state of the world,are irrelevant from the point of view of the prediction.The irrelevancy is meant in the sense of the second point in the discussion of Galileo’s theorem.8 As regards the present state of the world,such as the existence of the earth on which we live and on which Galileo’s experiments were performed,the existence of the sun and of all our surroundings,the laws of nature are entirely silent.It is in consonance with this,?rst,that the laws of nature can be used to predict future events only under exceptional circumstances when all the relevant determinants of the present state of the world are known.It is also in consonance with this that the construction of machines,the functioning of which he can foresee,constitutes the most spectacular accomplishment of the physicist.In these machines,the physicist creates a situation in which all the relevant coordinates are known so that the behavior of the machine can be predicted.Radars and nuclear reactors are examples of such machines.
The principal purpose of the preceding discussion is to point out that the laws of nature are all conditional statements and they relate only to a very small part of our knowledge of the world. Thus,classical mechanics,which is the best known prototype of a physical theory,gives the second derivatives of the positional coordinates of all bodies,on the basis of the knowledge of the positions,etc.,of these bodies.It gives no information on the existence,the present positions, or velocities of these bodies.It should be mentioned,for the sake of accuracy,that we discovered about thirty years ago that even the conditional statements cannot be entirely precise:that the conditional statements are probability laws which enable us only to place intelligent bets on future properties of the inanimate world,based on the knowledge of the present state.They do not allow us to make categorical statements,not even categorical statements conditional on the present state of the world.The probabilistic nature of the“laws of nature”manifests itself in the case of machines also,and can be veri?ed,at least in the case of nuclear reactors,if one runs them at very low power.However,the additional limitation of the scope of the laws of nature which follows from their probabilistic nature will play no role in the rest of the discussion. The Role of Mathematics in Physical Theories
Having refreshed our minds as to the essence of mathematics and physics,we should be in a better position to review the role of mathematics in physical theories.Naturally,we do use mathematics in everyday physics to evaluate the results of the laws of nature,to apply the conditional statements to the particular conditions which happen to prevail or happen to interest us.In order that this be possible,the laws of nature must already be formulated in mathematical language.However,the role of evaluating the consequences of already established theories is not the most important role of mathematics in physics.Mathematics,or,rather, applied mathematics,is not so much the master of the situation in this function:it is merely serving as a tool.
Mathematics does play,however,also a more sovereign role in physics.This was already implied in the statement,made when discussing the role of applied mathematics,that the laws of nature 8The writer feels sure that it is unnecessary to mention that Galileo’s theorem,as given in the text,does not exhaust the content of Galileo’s observations in connection with the laws of freely falling bodies.
must have been formulated in the language of mathematics to be an object for the use of applied mathematics.The statement that the laws of nature are written in the language of mathematics was properly made three hundred years ago;9it is now more true than ever before.In order to show the importance which mathematical concepts possess in the formulation of the laws of physics,let us recall,as an example,the axioms of quantum mechanics as formulated,explicitly, by the great physicist,Dirac.There are two basic concepts in quantum mechanics:states and observables.The states are vectors in Hilbert space,the observables self-adjoint operators on these vectors.The possible values of the observations are the characteristic values of the operators but we had better stop here lest we engage in a listing of the mathematical concepts developed in the theory of linear operators.
It is true,of course,that physics chooses certain mathematical concepts for the formulation of the laws of nature,and surely only a fraction of all mathematical concepts is used in physics. It is true also that the concepts which were chosen were not selected arbitrarily from a listing of mathematical terms but were developed,in many if not most cases,independently by the physicist and recognized then as having been conceived before by the mathematician.It is not true,however,as is so often stated,that this had to happen because mathematics uses the simplest possible concepts and these were bound to occur in any formalism.As we saw before, the concepts of mathematics are not chosen for their conceptual simplicity,even sequences of pairs of numbers are far from being the simplest concepts,but for their amenability to clever manipulations and to striking,brilliant arguments.Let us not forget that the Hilbert space of quantum mechanics is the complex Hilbert space,with a Hermitean scalar product.Surely to the unpreoccupied mind,complex numbers are far from natural or simple and they cannot be suggested by physical observations.Furthermore,the use of complex numbers is in this case not a calculational trick of applied mathematics but comes close to being a necessity in the formulation of the laws of quantum mechanics.Finally,it now begins to appear that not only complex numbers but so-called analytic functions are destined to play a decisive role in the formulation of quantum theory.I am referring to the rapidly developing theory of dispersion relations.
It is di?cult to avoid the impression that a miracle confronts us here,quite comparable in its striking nature to the miracle that the human mind can string a thousand arguments together without getting itself into contradictions,or to the two miracles of the existence of laws of nature and of the human mind’s capacity to divine them.The observation which comes closest to an explanation for the mathematical concepts’cropping up in physics which I know is Einstein’s statement that the only physical theories which we are willing to accept are the beautiful ones. It stands to argue that the concepts of mathematics,which invite the exercise of so much wit, have the quality of beauty.However,Einstein’s observation can at best explain properties of theories which we are willing to believe and has no reference to the intrinsic accuracy of the theory.We shall,therefore,turn to this latter question.
Is the Success of Physical Theories Truly Surprising?
A possible explanation of the physicist’s use of mathematics to formulate his laws of nature is that he is a somewhat irresponsible person.As a result,when he?nds a connection between two quantities which resembles a connection well-known from mathematics,he will jump at the conclusion that the connection is that discussed in mathematics simply because he does not know of any other similar connection.It is not the intention of the present discussion to refute the charge that the physicist is a somewhat irresponsible person.Perhaps he is.However, it is important to point out that the mathematical formulation of the physicist’s often crude experience leads in an uncanny number of cases to an amazingly accurate description of a large 9It is attributed to Galileo
class of phenomena.This shows that the mathematical language has more to commend it than being the only language which we can speak;it shows that it is,in a very real sense,the correct language.Let us consider a few examples.
The?rst example is the oft-quoted one of planetary motion.The laws of falling bodies became rather well established as a result of experiments carried out principally in Italy.These exper-iments could not be very accurate in the sense in which we understand accuracy today partly because of the e?ect of air resistance and partly because of the impossibility,at that time,to measure short time intervals.Nevertheless,it is not surprising that,as a result of their stud-ies,the Italian natural scientists acquired a familiarity with the ways in which objects travel through the atmosphere.It was Newton who then brought the law of freely falling objects into relation with the motion of the moon,noted that the parabola of the thrown rock’s path on the earth and the circle of the moon’s path in the sky are particular cases of the same mathematical object of an ellipse,and postulated the universal law of gravitation on the basis of a single,and at that time very approximate,numerical coincidence.Philosophically,the law of gravitation as formulated by Newton was repugnant to his time and to himself.Empirically,it was based on very scanty observations.The mathematical language in which it was formulated contained the concept of a second derivative and those of us who have tried to draw an osculating circle to a curve know that the second derivative is not a very immediate concept.The law of gravity which Newton reluctantly established and which he could verify with an accuracy of about4% has proved to be accurate to less than a ten thousandth of a per cent and became so closely associated with the idea of absolute accuracy that only recently did physicists become again bold enough to inquire into the limitations of its accuracy.10Certainly,the example of Newton’s law,quoted over and over again,must be mentioned?rst as a monumental example of a law, formulated in terms which appear simple to the mathematician,which has proved accurate be-yond all reasonable expectations.Let us just recapitulate our thesis on this example:?rst,the law,particularly since a second derivative appears in it,is simple only to the mathematician, not to common sense or to non-mathematically-minded freshmen;second,it is a conditional law of very limited scope.It explains nothing about the earth which attracts Galileo’s rocks,or about the circular form of the moon’s orbit,or about the planets of the sun.The explanation of these initial conditions is left to the geologist and the astronomer,and they have a hard time with them.
The second example is that of ordinary,elementary quantum mechanics.This originated when Max Born noticed that some rules of computation,given by Heisenberg,were formally identical with the rules of computation with matrices,established a long time before by mathematicians. Born,Jordan,and Heisenberg then proposed to replace by matrices the position and momentum variables of the equations of classical mechanics.They applied the rules of matrix mechanics to a few highly idealized problems and the results were quite satisfactory.However,there was,at that time,no rational evidence that their matrix mechanics would prove correct under more re-alistic conditions.Indeed,they say“if the mechanics as here proposed should already be correct in its essential traits.”As a matter of fact,the?rst application of their mechanics to a realistic problem,that of the hydrogen atom,was given several months later,by Pauli.This application gave results in agreement with experience.This was satisfactory but still understandable be-cause Heisenberg’s rules of calculation were abstracted from problems which included the old theory of the hydrogen atom.The miracle occurred only when matrix mechanics,or a math-ematically equivalent theory,was applied to problems for which Heisenberg’s calculating rules were meaningless.Heisenberg’s rules presupposed that the classical equations of motion had solutions with certain periodicity properties;and the equations of motion of the two electrons of the helium atom,or of the even greater number of electrons of heavier atoms,simply do not have 10See,for instance,R.H.Dicke,Am.Sci.,25(1959).
these properties,so that Heisenberg’s rules cannot be applied to these cases.Nevertheless,the calculation of the lowest energy level of helium,as carried out a few months ago by Kinoshita at Cornell and by Bazley at the Bureau of Standards,agrees with the experimental data within the accuracy of the observations,which is one part in ten million.Surely in this case we“got something out”of the equations that we did not put in.
The same is true of the qualitative characteristics of the“complex spectra,”that is,the spectra of heavier atoms.I wish to recall a conversation with Jordan,who told me,when the qualitative features of the spectra were derived,that a disagreement of the rules derived from quantum mechanical theory and the rules established by empirical research would have provided the last opportunity to make a change in the framework of matrix mechanics.In other words,Jordan felt that we would have been,at least temporarily,helpless had an unexpected disagreement occurred in the theory of the helium atom.This was,at that time,developed by Kellner and by Hilleraas.The mathematical formalism was too dear and unchangeable so that,had the miracle of helium which was mentioned before not occurred,a true crisis would have arisen. Surely,physics would have overcome that crisis in one way or another.It is true,on the other hand,that physics as we know it today would not be possible without a constant recurrence of miracles similar to the one of the helium atom,which is perhaps the most striking miracle that has occurred in the course of the development of elementary quantum mechanics,but by far not the only one.In fact,the number of analogous miracles is limited,in our view,only by our willingness to go after more similar ones.Quantum mechanics had,nevertheless,many almost equally striking successes which gave us the?rm conviction that it is,what we call,correct. The last example is that of quantum electrodynamics,or the theory of the Lamb shift.Whereas Newton’s theory of gravitation still had obvious connections with experience,experience entered the formulation of matrix mechanics only in the re?ned or sublimated form of Heisenberg’s prescriptions.The quantum theory of the Lamb shift,as conceived by Bethe and established by Schwinger,is a purely mathematical theory and the only direct contribution of experiment was to show the existence of a measurable e?ect.The agreement with calculation is better than one part in a thousand.
The preceding three examples,which could be multiplied almost inde?nitely,should illustrate the appropriateness and accuracy of the mathematical formulation of the laws of nature in terms of concepts chosen for their manipulability,the“laws of nature”being of almost fantas-tic accuracy but of strictly limited scope.I propose to refer to the observation which these examples illustrate as the empirical law of epistemology.Together with the laws of invariance of physical theories,it is an indispensable foundation of these theories.Without the laws of invariance the physical theories could have been given no foundation of fact;if the empirical law of epistemology were not correct,we would lack the encouragement and reassurance which are emotional necessities,without which the“laws of nature”could not have been successfully explored.Dr.R.G.Sachs,with whom I discussed the empirical law of epistemology,called it an article of faith of the theoretical physicist,and it is surely that.However,what he called our article of faith can be well supported by actual examples,many examples in addition to the three which have been mentioned.
The Uniqueness of the Theories of Physics
The empirical nature of the preceding observation seems to me to be self-evident.It surely is not a“necessity of thought”and it should not be necessary,in order to prove this,to point to the fact that it applies only to a very small part of our knowledge of the inanimate world.It is absurd to believe that the existence of mathematically simple expressions for the second derivative of the position is self-evident,when no similar expressions for the position itself or for the velocity
exist.It is therefore surprising how readily the wonderful gift contained in the empirical law of epistemology was taken for granted.The ability of the human mind to form a string of 1000conclusions and still remain“right,”which was mentioned before,is a similar gift.Every empirical law has the disquieting quality that one does not know its limitations.We have seen that there are regularities in the events in the world around us which can be formulated in terms of mathematical concepts with an uncanny accuracy.There are,on the other hand,aspects of the world concerning which we do not believe in the existence of any accurate regularities. We call these initial conditions.The question which presents itself is whether the di?erent regularities,that is,the various laws of nature which will be discovered,will fuse into a single consistent unit,or at least asymptotically approach such a fusion.Alternatively,it is possible that there always will be some laws of nature which have nothing in common with each other. At present,this is true,for instance,of the laws of heredity and of physics.It is even possible that some of the laws of nature will be in con?ict with each other in their implications,but each convincing enough in its own domain so that we may not be willing to abandon any of them. We may resign ourselves to such a state of a?airs or our interest in clearing up the con?ict between the various theories may fade out.We may lose interest in the“ultimate truth,”that is,in a picture which is a consistent fusion into a single unit of the little pictures,formed on the various aspects of nature.
It may be useful to illustrate the alternatives by an example.We now have,in physics,two theories of great power and interest:the theory of quantum phenomena and the theory of relativity.These two theories have their roots in mutually exclusive groups of phenomena. Relativity theory applies to macroscopic bodies,such as stars.The event of coincidence,that is,in ultimate analysis of collision,is the primitive event in the theory of relativity and de?nes a point in space-time,or at least would de?ne a point if the colliding panicles were in?nitely small.Quantum theory has its roots in the microscopic world and,from its point of view, the event of coincidence,or of collision,even if it takes place between particles of no spatial extent,is not primitive and not at all sharply isolated in space-time.The two theories operate with di?erent mathematical concepts,the four dimensional Riemann space and the in?nite dimensional Hilbert space,respectively.So far,the two theories could not be united,that is, no mathematical formulation exists to which both of these theories are approximations.All physicists believe that a union of the two theories is inherently possible and that we shall?nd it.Nevertheless,it is possible also to imagine that no union of the two theories can be found. This example illustrates the two possibilities,of union and of con?ict,mentioned before,both of which are conceivable.
In order to obtain an indication as to which alternative to expect ultimately,we can pretend to be a little more ignorant than we are and place ourselves at a lower level of knowledge than we actually possess.If we can?nd a fusion of our theories on this lower level of intelligence, we can con?dently expect that we will?nd a fusion of our theories also at our real level of intelligence.On the other hand,if we would arrive at mutually contradictory theories at a somewhat lower level of knowledge,the possibility of the permanence of con?icting theories cannot be excluded for ourselves either.The level of knowledge and ingenuity is a continuous variable and it is unlikely that a relatively small variation of this continuous variable changes the attainable picture of the world from inconsistent to consistent.11Considered from this point of view,the fact that some of the theories which we know to be false give such amazingly accurate results is an adverse factor.Had we somewhat less knowledge,the group of phenomena which 11This passage was written after a great deal of hesitation.The writer is convinced that it is useful,in epistemological discussions,to abandon the idealization that the level of human intelligence has a singular position on an absolute scale.In some cases it may even be useful to consider the attainment which is possible at the level of the intelligence of some other species.However,the writer also realizes that his thinking along the lines indicated in the text was too brief and not subject to su?cient critical appraisal to be reliable.
these“false”theories explain would appear to us to be large enough to“prove”these theories. However,these theories are considered to be“false”by us just for the reason that they are,in ultimate analysis,incompatible with more encompassing pictures and,if su?ciently many such false theories are discovered,they are bound to prove also to be in con?ict with each other. Similarly,it is possible that the theories,which we consider to be“proved”by a number of numerical agreements which appears to be large enough for us,are false because they are in con?ict with a possible more encompassing theory which is beyond our means of discovery.If this were true,we would have to expect con?icts between our theories as soon as their number grows beyond a certain point and as soon as they cover a su?ciently large number of groups of phenomena.In contrast to the article of faith of the theoretical physicist mentioned before, this is the nightmare of the theorist.
Let us consider a few examples of“false”theories which give,in view of their falseness,alarm-ingly accurate descriptions of groups of phenomena.With some goodwill,one can dismiss some of the evidence which these examples provide.The success of Bohr’s early and pioneering ideas on the atom was always a rather narrow one and the same applies to Ptolemy’s epicycles.Our present vantage point gives an accurate description of all phenomena which these more primi-tive theories can describe.The same is not true any longer of the so-called free-electron theory, which gives a marvellously accurate picture of many,if not most,properties of metals,semicon-ductors,and insulators.In particular,it explains the fact,never properly understood on the basis of the“real theory,”that insulators show a speci?c resistance to electricity which may be 1026times greater than that of metals.In fact,there is no experimental evidence to show that the resistance is not in?nite under the conditions under which the free-electron theory would lead us to expect an in?nite resistance.Nevertheless,we are convinced that the free-electron theory is a crude approximation which should be replaced,in the description of all phenomena concerning solids,by a more accurate picture.
If viewed from our real vantage point,the situation presented by the free-electron theory is irritating but is not likely to forebode any inconsistencies which are unsurmountable for us. The free-electron theory raises doubts as to how much we should trust numerical agreement between theory and experiment as evidence for the correctness of the theory.We are used to such doubts.
A much more di?cult and confusing situation would arise if we could,some day,establish a theory of the phenomena of consciousness,or of biology,which would be as coherent and convincing as our present theories of the inanimate world.Mendel’s laws of inheritance and the subsequent work on genes may well form the beginning of such a theory as far as biology is concerned.Furthermore,,it is quite possible that an abstract argument can be found which shows that there is a con?ict between such a theory and the accepted principles of physics.The argument could be of such abstract nature that it might not be possible to resolve the con?ict, in favor of one or of the other theory,by an experiment.Such a situation would put a heavy strain on our faith in our theories and on our belief in the reality of the concepts which we form. It would give us a deep sense of frustration in our search for what I called“the ultimate truth.”The reason that such a situation is conceivable is that,fundamentally,we do not know why our theories work so well.Hence,their accuracy may not prove their truth and consistency.Indeed, it is this writer’s belief that something rather akin to the situation which was described above exists if the present laws of heredity and of physics are confronted.
Let me end on a more cheerful note.The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve.We should be grateful for it and hope that it will remain valid in future research and that it will extend,for better or for worse,to our pleasure,even though perhaps also to our ba?ement,to wide branches of learning.
首届“教育教学技能大比武”总结 为期半个月的青年教师首届“教育教学技能大比武”活动已经圆满落下帷幕。参加本次比赛的教师都是38周岁以下的青年教师，比赛内容包括讲课、答辩、三笔字、演讲四个环节。这次活动在学校领导的大力支持下，在全体教师的努力配合下，在参赛教师积极参与、认真准备下，取得圆满成功。 回顾本次比赛活动，老师们无论是在个人综合素质、教材把握能力还是在课堂驾驭能力上都有精彩的展示，下面对本次活动做一个总结： 一、讲课赛环节 这十九位青年教师对此次比赛高度重视，认真备课、讲课，为我们呈现了一节节风格各异、亮点纷呈的课，主要呈现了一下几个特点： 1、备课充分、设计用心。 老师们在备课过程中，能深入钻研教材，做了大量充分的准备。老师们都精心设计导语，创设情境，千方百计地激发起学生强烈的求知欲，能够把知识和能力深入浅出又扎扎实实的传授给学生，每一节课都朴实无华，每一节课都独具匠心，比如：郑珊老师在讲授《图形的旋转》一课时，教学设计层次分明，抓住平移和旋转的特征明确其描述方法，在新授的过程中能够放手让学生自己思考-动手操作-小组交流-展示（说明描述），老师引导学生亲历学习过程，通过几个有效的追问，使自己体会掌握了学习内容。 2、教学扎实有效，注重基础训练。 老师们能够抓住教学目标，精心设计每一个环节，同时老师们十分注重基础训练，比如高年级语文老师在教学中注重字词的品读与指导，在阅读教学中，老师能通过阅读来领悟文本的内涵，例如王玉英讲述《梅花魂》一课，她更注重引导学生“品词、品句、品读”以此让学生以读明理，以读悟情，通过“品”字让学生真正体会到了外祖父为什么那么珍爱墨梅图，从而理解梅花的品行，上升到中国人的气节。语文中低年级教学中，教师注重字形的书写字文的理解和区别运用，比如赵彤霞老师执教《植物妈妈有办法》一课，能在文中恰到好处的让学生理解“许多”和“许”“多”的区别，并用“纷纷”说一句话。又比如赵志芳执教《秋天的雨》一课中，注重了“爽”字的书写指导，教学中注重句子的训练，让学生练说比喻句。 3、注重学生情感态度和学习习惯的培养。 注重学生情感态度和学习习惯的培养是成为这次比赛课的又一亮点。老师们在教学中，做到自始至终关注学生的情感，营造宽松、民主、和谐的教学气氛，尊重每个学生，积极鼓励他们在学习中的尝试，保护他们的自尊心和积极性。比如吴蕊霞老师的鼓励具有个性化，激励性的语言常挂嘴边，成为学生不断学习、创新不可缺乏的精神动力。同时在教学中注重学习习惯的培养，比如高月枝老师在授课的同时适时对学生进行了课常规的教育，整个一节课，教学秩序井然有序，对于刚上学两个星期的孩子真的很难得。 4、善用多媒体教学。 本次讲课赛几乎所有的老师都制作了精美实用的多媒体课件，追求既生动形象又快捷高效的教学效果。特别是赵丽和龚伟科两位老师用我们上学期培训的知识制作了白板课件。 5、教师素养良好。 通过这次比赛，我们欣喜地看到我校青年教师具备良好的教师基本素质。他们教态大方得体，语言清晰，具有较强的亲和力和应变能力。王敏、陈蓉等老师她们在课堂上文雅得体的教态，丰富的肢体语言以及亲切和蔼的微笑，都给我们留下了深刻的印象，深受学生的喜爱。 针对本次讲课赛反映出的问题，给老师们提出以下建议，跟老师们商榷：1、语文教学中，略读课文的教学教师应大胆放手学生，让学生充分展示自己。有感情的朗读，重在先理解再
The way 的用法 Ⅰ常见用法： 1)the way+ that 2)the way + in which（最为正式的用法） 3)the way + 省略（最为自然的用法） 举例：I like the way in which he talks. I like the way that he talks. I like the way he talks. Ⅱ习惯用法： 在当代美国英语中，the way用作为副词的对格，“the way+ 从句”实际上相当于一个状语从句来修饰整个句子。 1)The way =as I am talking to you just the way I’d talk to my own child. He did not do it the way his friends did. Most fruits are naturally sweet and we can eat them just the way they are—all we have to do is to clean and peel them. 2）The way= according to the way/ judging from the way The way you answer the question, you are an excellent student. The way most people look at you, you’d think trash man is a monster. 3）The way =how/ how much No one can imagine the way he missed her. 4）The way =because
教师即兴演讲题目之63个话题 来源：思雨教育资源网|教学资源|课件论文|作文作者：无边思雨发表日期：2009-5-30 13:16:19 阅读次数： 910 查看权限：普通文章 1、如何维护班集体荣誉？ 2、如何看待学生时代早恋问题？ 3、成人与成才二者是怎样的关系？结合实例说明自己的观点。 4、不同地域、不同背景、不同习惯的同学之间该如何相处？ 5、怎样面对学习、生活中遇到的挫折？ 6、你最崇拜的人是谁？“名人”还是自己？ 7、你认为我们是否应有感恩之心？感恩于谁？ 8、你希望自己会是怎样一位老师？你会如何教育自己的学生？ 9、“言行、仪表”与个人的发展。 10、如今继续提倡“勤俭、节约”作风是否已过时？ 11、在各种资料、媒体中常讲张扬个性，你认为我们该张扬什么样的个性？ 12、三轮车工人方尚礼自己生活的如乞丐，却将自己蹬车收入的35万多元用来资助失学儿童，当病重时，社会捐助给他治病的钱，也被他捐给了希望工程。你对方尚礼的这种行为有何评述？ 13、电视广告不宜过多 14、保护环境是每个人的责任 15、我中学时代的一个朋友 16、世界需要热心肠 17、向权威挑战 18、2008年的我 19、我爱电视广告 20、我的母亲 21、尊重是孩子成长的基石 22、如何培养学生的好奇心 23、推广普通话 24、“恶语伤人六月寒” 25、我心中的偶像 26、假如我是画家 27、童年趣事 28、珍惜现在 29、我最爱看的电视节目 30、有人认为老师是不断燃烧的蜡烛，你认为呢？ 31、新课程背景下良好师生场的营造。 32、让谐趣幽默走进我们的课堂。 33、阅读教学中如何开展有效的对话教学？ 34、如何正确处理价值取向和个性化阅读的关系？ 35、新课程背景下一堂好课的标准是什么？ 36、“语文教学工具性与人文性统一”的内涵是什么？ 37、如何实践语文教学的人文性和工具性的“统一”？ 38、如何挖掘教材资源，准确选点，扎实训练？
The way的用法及其含义（二） 二、the way在句中的语法作用 the way在句中可以作主语、宾语或表语： 1.作主语 The way you are doing it is completely crazy.你这个干法简直发疯。 The way she puts on that accent really irritates me. 她故意操那种口音的样子实在令我恼火。The way she behaved towards him was utterly ruthless. 她对待他真是无情至极。 Words are important, but the way a person stands, folds his or her arms or moves his or her hands can also give us information about his or her feelings. 言语固然重要,但人的站姿,抱臂的方式和手势也回告诉我们他(她)的情感。 2.作宾语 I hate the way she stared at me.我讨厌她盯我看的样子。 We like the way that her hair hangs down.我们喜欢她的头发笔直地垂下来。 You could tell she was foreign by the way she was dressed. 从她的穿著就可以看出她是外国人。 She could not hide her amusement at the way he was dancing. 她见他跳舞的姿势，忍俊不禁。 3.作表语 This is the way the accident happened.这就是事故如何发生的。 Believe it or not, that's the way it is. 信不信由你, 反正事情就是这样。 That's the way I look at it, too. 我也是这么想。 That was the way minority nationalities were treated in old China. 那就是少数民族在旧中
定冠词the的用法： 定冠词the与指示代词this ,that同源,有“那(这)个”的意思,但较弱,可以和一个名词连用,来表示某个或某些特定的人或东西. (1)特指双方都明白的人或物 Take the medicine.把药吃了. (2)上文提到过的人或事 He bought a house.他买了幢房子. I've been to the house.我去过那幢房子. (3)指世界上独一无二的事物 the sun ,the sky ,the moon, the earth (4)单数名词连用表示一类事物 the dollar 美元 the fox 狐狸 或与形容词或分词连用,表示一类人 the rich 富人 the living 生者 (5)用在序数词和形容词最高级,及形容词等前面 Where do you live?你住在哪? I live on the second floor.我住在二楼. That's the very thing I've been looking for.那正是我要找的东西. (6)与复数名词连用,指整个群体 They are the teachers of this school.(指全体教师) They are teachers of this school.(指部分教师) (7)表示所有,相当于物主代词,用在表示身体部位的名词前 She caught me by the arm.她抓住了我的手臂. (8)用在某些有普通名词构成的国家名称,机关团体,阶级等专有名词前 the People's Republic of China 中华人民共和国 the United States 美国 (9)用在表示乐器的名词前 She plays the piano.她会弹钢琴. (10)用在姓氏的复数名词之前,表示一家人 the Greens 格林一家人(或格林夫妇) (11)用在惯用语中 in the day, in the morning... the day before yesterday, the next morning... in the sky... in the dark... in the end... on the whole, by the way...
“tｈｅwａｙ+从句”结构的意义及用法 首先让我们来看下面这个句子: Ｒead the foｌloｗｉnｇpassagｅａnd talkａbout ｉt wi ｔh your classmaｔes．Try tｏｔeｌl whaｔyｏu thiｎk ｏf Tom aｎd ｏｆｔhe ｗay the chiｌｄrenｔrｅated ｈim. 在这个句子中，ｔhe waｙ是先行词,后面是省略了关系副词that或in whｉch的定语从句。 下面我们将叙述“the ｗaｙ+从句”结构的用法。 1.tｈe wａy之后，引导定语从句的关系词是tｈat而不是hoｗ,因此，<<现代英语惯用法词典＞＞中所给出的下面两个句子是错误的：Ｔhｉs is ｔｈeｗayｈowｉtｈａppened. This is the way how he ａlwａｙs treats me. 2．在正式语体中,thaｔ可被in which所代替;在非正式语体中，ｔhat则往往省略。由此我们得到theｗay后接定语从句时的三种模式：1) tｈe ｗaｙ＋ｔhａt-从句２）the way +ｉn whiｃh－从句3) the ｗay +从句 例如：Ｔｈe way(in whiｃh ，thａt) ｔhｅｓｅｃomｒade ｓloｏｋａｔｐrobｌems is wrong．这些同志看问题的方法
不对。 Ｔｈｅｗａy(that ,ｉn ｗhiｃh)yoｕ’ｒe doinｇit is comple ｔeｌy crａzy.你这么个干法,简直发疯。 Wｅａdmiｒｅd him for thｅｗay ｉｎｗhｉch he fａｃeｓdiｆficultieｓ． Waｌlａｃe ａｎd Ｄarwiｎｇreed ｏn the way ｉｎwhi ｃh ｄｉfｆｅrｅnt forms ｏf life had ｂegｕn.华莱士和达尔文对不同类型的生物是如何起源的持相同的观点。 Thｉs is ｔｈe ｗaｙ（tｈａｔ) hｅdｉd it. I lｉkeｄｔhe waｙ(ｔhat) ｓｈeｏｒganized ｔhe ｍeetｉng． 3.theｗay(tｈat)有时可以与hｏw(作“如何”解）通用。例如： That’s tｈe ｗaｙ(tｈaｔ) shｅspoke. = Tｈat’s how shｅspoke.
表示“方式”、“方法”，注意以下用法： 1.表示用某种方法或按某种方式，通常用介词in(此介词有时可省略)。如： Do it (in) your own way. 按你自己的方法做吧。 Please do not talk (in) that way. 请不要那样说。 2.表示做某事的方式或方法，其后可接不定式或of doing sth。 如： It’s the best way of studying [to study] English. 这是学习英语的最好方法。 There are different ways to do [of doing] it. 做这事有不同的办法。 3.其后通常可直接跟一个定语从句(不用任何引导词)，也可跟由that 或in which 引导的定语从句，但是其后的从句不能由how 来引导。如： 我不喜欢他说话的态度。 正：I don’t like the way he spoke. 正：I don’t like the way that he spoke. 正：I don’t like the way in which he spoke. 误：I don’t like the way how he spoke. 4.注意以下各句the way 的用法： That’s the way (=how) he spoke. 那就是他说话的方式。 Nobody else loves you the way(=as) I do. 没有人像我这样爱你。 The way (=According as) you are studying now, you won’tmake much progress. 根据你现在学习情况来看，你不会有多大的进步。 2007年陕西省高考英语中有这样一道单项填空题： ——I think he is taking an active part insocial work. ——I agree with you_____. A、in a way B、on the way C、by the way D、in the way 此题答案选A。要想弄清为什么选A，而不选其他几项，则要弄清选项中含way的四个短语的不同意义和用法，下面我们就对此作一归纳和小结。 一、in a way的用法 表示：在一定程度上，从某方面说。如： In a way he was right.在某种程度上他是对的。注：in a way也可说成in one way。 二、on the way的用法 1、表示：即将来(去)，就要来(去)。如： Spring is on the way.春天快到了。 I'd better be on my way soon.我最好还是快点儿走。 Radio forecasts said a sixth-grade wind was on the way.无线电预报说将有六级大风。 2、表示：在路上，在行进中。如： He stopped for breakfast on the way.他中途停下吃早点。 We had some good laughs on the way.我们在路上好好笑了一阵子。 3、表示：(婴儿)尚未出生。如： She has two children with another one on the way.她有两个孩子，现在还怀着一个。 She's got five children，and another one is on the way.她已经有5个孩子了，另一个又快生了。 三、by the way的用法
青年教师朗诵比赛活动方案 （2014----2015）学年度下学期 一、活动目的： 学校是推广普通话，规范语言文字的主阵地，教师作为推广普通话的中坚力量有着不可忽视的重要作用。因此，为了加强教师基本功训练，提升教师的朗读水平，教导处根据语言文字规范化活动计划，开展以“朗读美文展我风采”的教师朗诵比赛。通过教师美文朗读比赛，提高我校青年教师普通话水平，营造浓厚的校园读书氛围，提升教师教学基本功，促使教师重视朗读教学，促进学生健康和谐发展。 二、活动组织：教导处 三、具体活动安排： 1、培训时间：6月8日（周一）下午14:30 2、比赛时间：6月15日（周一）下午14:30 3、比赛地点：四楼舞蹈室 4、参赛人员：35岁以下（含35岁）青年教师必须参加，同时欢迎35岁以上教师参加。 5、比赛内容：作品自选，体裁不限（不少于三分钟） 6、比赛形式：可配乐，参赛人员独立诵读。 7、评委：黄冬梅蒋丽丽郭艳华贺芳刘忠霞冷静武玉德 8、分数统计：王辉赵慧贤
9、主持：徐金凤 四、活动程序： 1、学校将在赛前一周邀请校长对参赛人员进行培训。 2、参赛教师提前十分钟到达比赛场地，做好准备工作。 3、14:40正式进行比赛，按抽签顺序进行。 4、评分办法：比赛采取现场评分的办法，满分10分，比赛结束后，进行分数汇总、统计，取平均分，宣布比赛成绩。 5、校长点评并作总结。 五、设奖情况： 本次比赛将设一等奖2名，二等奖3名，三等奖5名，优秀奖若干名。比赛成绩计入年末教师量化考核。 六、朗诵比赛评分标准 （一）、主题内容（2分） 1、内容（1分）：题材不限，内容健康向上；充实生动，有真情实意 2、主题（1分）：寓意深刻，富有感召力 （二）、普通话（3分） 1、发音（1分）：语音准确1分，较准确0.8分，基本准确0.5分，不准确不得分。 2、语速（1分）：语速恰当、声音洪亮，表达自然流畅1分，因不熟练，每停顿一次扣0.1分。
青年教师基本功大赛即兴演讲题目【题目1】我的兴趣爱好【题目2】谈谈内心和谐【题目3】人最难超越的高度就是自己【题目4】我的价值观【题目5】谈谈与人相处【题目6】坚守心灵的一方沃土【题目7】给快乐找个理由【题目8】年轻 没有什么不可以【题目9】心底无私天地宽【题目10】人是需要一点精神的【题目11】我们与时代同行【题目12】生活从“心”开始【题目13】让更多的人快乐 【题目14】面对繁杂的教学工作 你如何调整心态 【题目15】和谐、健康、快乐【题目16】我喜爱的书刊【题目17】你如何发展自己的专业弱点【题目18】善待自己 呵护希望【题目18】.上公开课对一个教师的成长的作用【题目19】培养积极心态 感悟责任人生【题目24】永不言弃 我心永恒 准备时间 3分钟 【题目25】.你怎样做个身心健康的老师【题目26】你如何看待家长满意工程 【题目27】新课程执行过程中 你碰到最棘手的问题是什么【题目28】课堂教学中 你最关注的是什么【题目29】你希望学校领导关心青年教师哪些方面【题目30】谈谈自己的业余生活【题目31】简评最近的工作情况。【题目32】怎样才能提高教师的凝聚力。【题目33】.谈谈做班主任的心得【题目34】.你怎样定义教师【题目35】简介杨森中学【题目36】.点评一位我校的优秀教师【题目37】.如何看待家长的不理解【题目38】.谈谈卫生与健康【题目39】谈谈我校的环境. 【题目40】谈谈如何管理学生【题目41】谈谈你对职业道德的认识【题目42】我参加校本研修之感想。【题目43】“依法治教 注重服务 着力塑造行业形象” 请你谈谈你的设想【题目44】.如何发挥你校师生之特长 【题目45】.怎样调动老师的工作积极性 【题目46】.谈谈你对校本教研的看法。【题目47】.我是怎样备课的。【题目48】.维持校门口的秩序 我的一点想法。【题目49】如何丰富教师的业余生活 缓解教师的心理压力 【题目50】谈谈你对节日文化的认识【题目51】学校活动很多的情况下 你如何调节自己的心态 【题目52】德育倡导“全面德育 全员德育” 请你谈谈自己的理解。【题目53】如何让家长尊重教师 【题目54】你认为提高教育质量应从哪里抓起【题目55】从哪些方面帮助班主任管理学生篇二：教师即兴演讲题目之63个话题 教师即兴演讲题目之63个话题 来源：思雨教育资源网|教学资源|课件论文|作文作者：无边思雨发表日期：2009-5-30 13:16:19 阅读次数： 910 查看权限：普通文章 1、如何维护班集体荣誉？ 2、如何看待学生时代早恋问题？ 3、成人与成才二者是怎样的关系？结合实例说明自己的观点。 4、不同地域、不同背景、不同习惯的同学之间该如何相处？ 5、怎样面对学习、生活中遇到的挫折？ 6、你最崇拜的人是谁？“名人”还是自己？ 7、你认为我们是否应有感恩之心？感恩于谁？ 8、你希望自己会是怎样一位老师？你会如何教育自己的学生？ 9、“言行、仪表”与个人的发展。 10、如今继续提倡“勤俭、节约”作风是否已过时？ 11、在各种资料、媒体中常讲张扬个性，你认为我们该张扬什么样的个性？ 12、三轮车工人方尚礼自己生活的如乞丐，却将自己蹬车收入的35万多元用来资助失学儿童，当病重时，社会捐助给他治病的钱，也被他捐给了希望工程。你对方尚礼的这种行为有何评述？ 13、电视广告不宜过多 14、保护环境是每个人的责任
The way的用法及其含义（一） 有这样一个句子：In 1770 the room was completed the way she wanted. 1770年，这间琥珀屋按照她的要求完成了。 the way在句中的语法作用是什么？其意义如何？在阅读时，学生经常会碰到一些含有the way 的句子，如：No one knows the way he invented the machine. He did not do the experiment the way his teacher told him.等等。他们对the way 的用法和含义比较模糊。在这几个句子中，the way之后的部分都是定语从句。第一句的意思是，“没人知道他是怎样发明这台机器的。”the way的意思相当于how；第二句的意思是，“他没有按照老师说的那样做实验。”the way 的意思相当于as。在In 1770 the room was completed the way she wanted.这句话中，the way也是as的含义。随着现代英语的发展，the way的用法已越来越普遍了。下面，我们从the way的语法作用和意义等方面做一考查和分析： 一、the way作先行词，后接定语从句 以下3种表达都是正确的。例如：“我喜欢她笑的样子。” 1. the way+ in which +从句 I like the way in which she smiles. 2. the way+ that +从句 I like the way that she smiles. 3. the way + 从句(省略了in which或that) I like the way she smiles. 又如：“火灾如何发生的，有好几种说法。” 1. There were several theories about the way in which the fire started. 2. There were several theories about the way that the fire started.
教师基本功是教师从事教育教学工作必须具备的最基本的职业技能。它包括通用于所有教师的一般基本功，也包括学科教学和教育工作的基本功。教师基本功是加强青年教师职业道德建设的一项重要内容，也是教师从事教育教学工作必须具备的最基本的职业技能。如果说教学是技术加艺术，那么这种技术和艺术主要表现在教师课堂教学的基本功上面。它是教师素质的重要表现，也是教学成败的关键。过去所说的教师基本功，无非是三字一画（钢笔、毛笔、粉笔字和简笔画）和语文基础知识、口头表达能力等，再加上一些专业学科的基本功（音乐、体育、美术等）。在新一轮的课程改革中，需要我们重新看待教师的教学基本功。随着时代的发展，教师基本功的含义越来越广，教 师基本功包括的范围越来越大。下面我谈谈自己对教师应该具备的基本功的认识。 一、为人师表教师基本功应以德为先，教师的基本素质首当其冲的是师德素质。 我认为教师首先要有高尚的师德，只有思想上以学生为本，有做名师的愿望，至少有一个积极健康的心态，才能练好基本功。 1、有理想，有事业心。 2、以身作则学校无小事，处处皆教育，教师一言一行都会对学生造成影响。 二、爱的能力教师做的是人的工作，应该有人文素质，在爱
人过程中进行教育教学工作。爱学生也是一种技能，爱他们，使他们 容易、愉悦接受。 三、表达能力. 1、语言表达普通话是教师的职业语言，教师能用普通话进 行教学，普通话一般应达到国家语委制定的《普通话水平测试》二级水平。 2、文字表达教师的工作比较繁重，但是要学会反思和总结， 把心得体会写出来，才能少走弯路，更快进步，摆脱烦琐；才能轻松、高效的工作。 四、动手能力. 1、三笔一画这是传统意义的教师基本功。 2、板书板书不仅表现出一位教师上课的基本功，而且也体现教师的教学态度乃至性格。 3、运用、制作教具使用、制作教具方面，能按教学要求，正确使用教具；能就地取材，制作简易的教具。 4、现代信息技术的掌握和运用。 5、演示一般教师的演示指教态，教师也要做一个演员。 五、备课能力
way 的用法 【语境展示】 1. Now I’ll show you how to do the experiment in a different way. 下面我来演示如何用一种不同的方法做这个实验。 2. The teacher had a strange way to make his classes lively and interesting. 这位老师有种奇怪的办法让他的课生动有趣。 3. Can you tell me the best way of working out this problem? 你能告诉我算出这道题的最好方法吗？ 4. I don’t know the way (that / in which) he helped her out. 我不知道他用什么方法帮助她摆脱困境的。 5. The way (that / which) he talked about to solve the problem was difficult to understand. 他所谈到的解决这个问题的方法难以理解。 6. I don’t like the way that / which is being widely used for saving water. 我不喜欢这种正在被广泛使用的节水方法。 7. They did not do it the way we do now. 他们以前的做法和我们现在不一样。 【归纳总结】 ●way作“方法，方式”讲时，如表示“以……方式”，前面常加介词in。如例1； ●way作“方法，方式”讲时，其后可接不定式to do sth.，也可接of doing sth. 作定语，表示做某事的方法。如例2，例3；
教师基本功是什么1 我们常说“教学基本功”如何如何，多指教师的专业功底，教学基本技能，教学方法以及由此产生的教学效果等等，放在一个讨论教师质量和教育教学质量的背景下，我们是不是关注一下：什么是教师基本功呢？ 基本素质 教师的基本素质首当其冲的是师德素质。师德不能等同于职业道德，但却函盖职业道德。我觉得职业道德主要是针对物品或没生命的，或有生命也不是传道授业与做人思想工作的。教师的职业道德重要的在于“师”字上，即为人师的职业道德。只是时下还有多少人能够有称职的师德呢？！当下的教育环境下，教师一方面普遍出现职业倦怠，一方面却又师德开始退化！教师的现状让人担忧！ 我觉得，教师的基本素质应还包括人文素养，没有人文素养的教师眼中根本就不会有“人”的存在，也就不会在新课程中体现“以人为本”的理念，更不会在课堂上有“生命的气息”！我觉得人文素养应该尊重生命、尊重人的尊严，还要包括带头遵守社会文明公约、法律法规等，并成为践行的时代先锋。也就是说，教师还要在遵守社会文明等方面真正为人师表！ 基本知识 教师职业的特殊性，必然要求每一个教师要具备一定的基本知识，即包括教育理论、学科知识、心理学知识等。教师教育理论的丰厚与否往往束缚一个教师的发展与理论素养的高低，甚至影响到教师的教育思想与个人成长;而学科知识除了学科的相关基础知识外，还应包括学科的前沿知识；因为现在的学生压力大，心理又非常脆弱，这就给教师的教育工作增加了难度，因此，教师的基本知识应该要有心理辅导的知识，再说，当下的教师工作压力大，许多教师心理也存在一定的问题，他们本身更需要心理的自我调适能力。 基本能力 教师应具备的基本能力是什么呢？我认为应该是学习能力、科研能力、解决问题能力、写作能力、组织教学能力、协作能力等。 知识日新月异，特别是网络的盛行，让知识的传播与创新更快，因此，教师如果没有学习能力，就不能与时俱进，便会成为时代的落后者，这会影响到教师自身的发展与教育水平高低。况且，现在对于终身教育或终身学习理念的倡导，作为一名教师更应该成为这一理念的先驱。 科研能力是不是教师的必备能力？或者说教师要不要搞教育科研？我觉得不一定每一个教师都要成为研究型教师与专家型教师，但具备一定的教育科研能力，或了解教育科研的方法，或参与并体验科学研究的过程，应该是教师要积极投入的一种体验。而且，当前新课程提倡的探究性学习或研究性学习，本身就是要培养学生的科学素养与科学精神！如果教师不具备
小学英语教师基本功比赛朗读材料-MY DREAM My Dream Everyone has a lot of dreams. Some people want to be rich, dreaming of becoming millionaires [m?lj?'ne?] overnight. Others want to be famous, dreaming of suddenly jumping to great fame. I have a lot of dreams,too. When I was a young girl, I dreamed of becoming a scientist like Hua Iuogen in future. However, I knew very well that I could not succeed without painstaking ['pe?nzte?k??]efforts. So I studied hard in the middle school and college in order to attain my goal. After graduating from college, I found a job as a teacher. Although I was very busy with teaching, I never gave up my goal. I read a lot of books to get more knowledge. I made experiments to practice and apply what I had learnt from the books. Sometimes, I was so deeply indulged [?n'd?ld?] in my research that I forgot my meals and time. Now I have made great progress. Several of my research papers have been published. The methods ['meθ?d] proposed in my papers have been proven
t h e-w a y-的用法
The way 的用法 "the way+从句"结构在英语教科书中出现的频率较高, the way 是先行词, 其后是定语从句.它有三种表达形式:1) the way+that 2)the way+ in which 3)the way + 从句(省略了that或in which),在通常情况下, 用in which 引导的定语从句最为正式,用that的次之,而省略了关系代词that 或 in which 的, 反而显得更自然,最为常用.如下面三句话所示,其意义相同. I like the way in which he talks. I like the way that he talks. I like the way he talks. 一.在当代美国英语中,the way用作为副词的对格,"the way+从句"实际上相当于一个状语从句来修饰全句. the way=as 1)I'm talking to you just the way I'd talk to a boy of my own. 我和你说话就象和自己孩子说话一样. 2)He did not do it the way his friend did. 他没有象他朋友那样去做此事. 3)Most fruits are naturally sweet and we can eat them just the way they are ----all we have to do is clean or peel them . 大部分水果天然甜润,可以直接食用,我们只需要把他们清洗一下或去皮.
教师基本功即兴演讲 【篇一：青年教师基本功大赛即兴演讲题目】 青年教师基本功大赛即兴演讲题目【题目1】我的兴趣爱好【题目2】谈谈内心和谐【题目3】人最难超越的高度就是自己【题目4】 我的价值观【题目5】谈谈与人相处【题目6】坚守心灵的一方沃 土【题目7】给快乐找个理由【题目8】年轻?没有什么不可以 【题目9】心底无私天地宽【题目10】人是需要一点精神的【题目11】我们与时代同行【题目12】生活从“心”开始【题目13】让更 多的人快乐?【题目14】面对繁杂的教学工作?你如何调整心态 ?【题目15】和谐、健康、快乐【题目16】我喜爱的书刊【题目17】你如何发展自己的专业弱点【题目18】善待自己?呵护希望 【题目18】.上公开课对一个教师的成长的作用【题目19】培养积 极心态?感悟责任人生【题目24】永不言弃?我心永恒?准备时间 ?3分钟?【题目25】.你怎样做个身心健康的老师【题目26】你如何看待家长满意工程?【题目27】新课程执行过程中?你碰到最棘 手的问题是什么【题目28】课堂教学中?你最关注的是什么【题目29】你希望学校领导关心青年教师哪些方面【题目30】谈谈自己的 业余生活【题目31】简评最近的工作情况。【题目32】怎样才能 提高教师的凝聚力。【题目33】.谈谈做班主任的心得【题目34】. 你怎样定义教师【题目35】简介杨森中学【题目36】.点评一位我 校的优秀教师【题目37】.如何看待家长的不理解【题目38】.谈谈 卫生与健康【题目39】谈谈我校的环境. 【题目40】谈谈如何管理 学生【题目41】谈谈你对职业道德的认识【题目42】我参加校本 研修之感想。【题目43】“依法治教?注重服务?着力塑造行业形 象”?请你谈谈你的设想【题目44】.如何发挥你校师生之特长? 【题目45】.怎样调动老师的工作积极性?【题目46】.谈谈你对校 本教研的看法。【题目47】.我是怎样备课的。【题目48】.维持校 门口的秩序?我的一点想法。【题目49】如何丰富教师的业余生活 ?缓解教师的心理压力?【题目50】谈谈你对节日文化的认识【题 目51】学校活动很多的情况下?你如何调节自己的心态?【题目52】德育倡导“全面德育?全员德育”?请你谈谈自己的理解。【题目53】如何让家长尊重教师?【题目54】你认为提高教育质量应从哪里抓 起【题目55】从哪些方面帮助班主任管理学生 【篇二：教师基本功即兴演讲需要准备几分钟】
way的用法总结大全 way的用法你知道多少，今天给大家带来way的用法，希望能够帮助到大家，下面就和大家分享，来欣赏一下吧。 way的用法总结大全 way的意思 n. 道路,方法,方向,某方面 adv. 远远地，大大地 way用法 way可以用作名词 way的基本意思是“路,道,街,径”,一般用来指具体的“路,道路”,也可指通向某地的“方向”“路线”或做某事所采用的手段,即“方式,方法”。way还可指“习俗,作风”“距离”“附近,周围”“某方面”等。 way作“方法,方式,手段”解时,前面常加介词in。如果way前有this, that等限定词,介词可省略,但如果放在句首,介词则不可省略。
way作“方式,方法”解时,其后可接of v -ing或to- v 作定语,也可接定语从句,引导从句的关系代词或关系副词常可省略。 way用作名词的用法例句 I am on my way to the grocery store.我正在去杂货店的路上。 We lost the way in the dark.我们在黑夜中迷路了。 He asked me the way to London.他问我去伦敦的路。 way可以用作副词 way用作副词时意思是“远远地,大大地”,通常指在程度或距离上有一定的差距。 way back表示“很久以前”。 way用作副词的用法例句 It seems like Im always way too busy with work.我工作总是太忙了。 His ideas were way ahead of his time.他的思想远远超越了他那个时代。 She finished the race way ahead of the other runners.她第一个跑到终点,远远领先于其他选手。 way用法例句
t h e_w a y的用法大全
The way 在the way+从句中, the way 是先行词, 其后是定语从句.它有三种表达形式:1) the way+that 2)the way+ in which 3)the way + 从句(省略了that或in which),在通常情况下, 用in which 引导的定语从句最为正式,用that的次之,而省略了关系代词that 或 in which 的, 反而显得更自然,最为常用.如下面三句话所示,其意义相同. I like the way in which he talks. I like the way that he talks. I like the way he talks. 如果怕弄混淆，下面的可以不看了 另外，在当代美国英语中,the way用作为副词的对格,"the way+从句"实际上相当于一个状语从句来修饰全句. the way=as 1)I'm talking to you just the way I'd talk to a boy of my own. 我和你说话就象和自己孩子说话一样. 2)He did not do it the way his friend did. 他没有象他朋友那样去做此事. 3)Most fruits are naturally sweet and we can eat them just the way they are ----all we have to do is clean or peel them . 大部分水果天然甜润,可以直接食用,我们只需要把他们清洗一下或去皮. the way=according to the way/judging from the way 4)The way you answer the qquestions, you must be an excellent student. 从你回答就知道,你是一个优秀的学生. 5)The way most people look at you, you'd think a trashman was a monster. 从大多数人看你的目光中,你就知道垃圾工在他们眼里是怪物. the way=how/how much 6)I know where you are from by the way you pronounce my name. 从你叫我名字的音调中,我知道你哪里人. 7)No one can imaine the way he misses her. 人们很想想象他是多么想念她. the way=because 8) No wonder that girls looks down upon me, the way you encourage her. 难怪那姑娘看不起我, 原来是你怂恿的