Treatment of “Fragile Knowledge Syndrome”

Nanjing Normal University Hao Jinghua

“Fragile knowledge syndrome”[1],proposed by David Perkins,is a metaphorical concept reflects that mastery of knowledge is inadequate.In this paper,various concrete instances are enumerated and the “etiologies” of this syndrome are discussed in aims to be put forward the treatment methods.

1.Manifestation of “fragile knowledge syndrome”[2]

Perkins (1992) noticed that there are three notable issues on knowledge learning.

(1) Inert knowledge

It allows students to remember information when tested,but does not give them the ability to apply it outside of classroom.

(2) Naive knowledge

It refers to knowledge that lets student rely on simple explanations or formulas to provide the answer,but doesn't require them to apply knowledge in flexible ways.

(3) Ritual knowledge

It is a substitution of routines that work well in a classroom for real knowledge;students go through the motions expected in school but see no applications to the world beyond the classroom.

The “fragile knowledge syndrome” proposed by Perkins is not only real in Chinese students' classroom,but statistical significance observed.There are some instances as follows.

(1) Take inert knowledge for an example.When I have lesson in the morning,I usually ask those students to hand up if they did not have breakfast.It is surprising that more than one third of the college students don't have breakfast.Even more shocking is that almost all of them could give the exact answers about the nutritional elements,including carbohydrates,protein,fat,vitamins,minerals,water and cellulose.

(2) Take naive knowledge for an example.There are two questions.

①Float and sink of a piece of apple—If we cut a piece from an apple and drop it into a cup of water,does it float on the surface? Many people think it depends on the size of the piece (it means that the bigger one such as a whole apple sinks while the small one floats).

②The change of the quality of the steel wool before and after it is lighted—Is there any change of the quality of steel wool after inflammation? [3]

(3) Take Ritual knowledge for an example.The question I often ask to primary school students when I do fieldwork.School bus are each capable of carrying 36 persons,then how many buses are needed to carry 1128 students? More than one fifth students answer that there should be 31 buses with 12 students left.

It seems that “fragile knowledge syndrome” is not the privilege of the underachievers,even those meritorious students,who do well in examination.But there is no more evidences which could prove that they still remember those knowledge one or two weeks later,without mention the knowledge in daily life.Gardner also realized this:“Even those well-trained students with great potentials...don't show their clear understanding on the materials and concepts which have been focused on.”(Gardner,2006)[4]

Considerable circumstantial evidence suggests that the knowledge students are learning in school is fragile.It proves that students do not grasp meaning and cannot apply what is studied.

Obviously,“fragile knowledge syndrome” is not the effect that teachers expected.However,we have to point out that it is mainly the result of teaching.

2.Analysis on the reasons lead to “fragile knowledge syndrome”

2.1.Misapprehension on“understanding”

Every teacher knows the importance of “understanding”.But what is understanding exactly? I'm afraid that most of teachers feel it difficult to express in words.Some experts describe understanding as a kind of teaching goal which “everyone is using while nobody really knows”.Since 1960s,along with the research of the cognitive learning theory springing up in American theoretical circle,many researchers were interested in meaning of “understanding”.What is understanding？Why pursue understanding? How to evaluate whether the students actually had understood or not？How to teach for understanding? ...Ausubel (1967)[5],Bloom (1956,Krathwohl et al.,1964)[6] did great contributions on studies about “understanding”,Wilkins and Mitchell(Hammond et al.,1966)[7] also did some deep research about this concept.“Harvard Project Zero” proposed four dimensions and their characters about understanding.

These four dimensions emphasized on using understanding as a tool (not the facts or concepts about understanding).Researchers from Harvard point out that if we want to apply this,we need to do four ways of transformation.Firstly,the concerns which originally only focus on the reality about world should be shifted to the conceptual net which has more wider,well organized and currently reliable net consists of instances and generalizations. Secondly,individuals should construct these knowledge based on more credibility and validation of public.Thirdly,it should pay more attention to promote exploring some specific questions and applying the production of knowledge.Finally,individuals should find appropriate ways of transferring and sharing on knowledge.[8]

These findings are of great significance as Chinese researchers comprehend and evaluate the concept of understanding.It is telling us that understanding is absolutely not only the literal meaning,like a parrot.Knowledge in itself does not guarantee understanding.People can acquire knowledge.Mature understanding(deep understanding)includes the abilities of knowing not only the phenomenon and result,but also the reason,the ability of using knowledge in the context of the general subject area,and make generalizations related to the subject and the capability of expressing in various ways,going beyond superficial understanding.

The importance of understanding is,as a study finds[9],the ability to use knowledge in new context,that is,the ability of transferring of knowledge,depends to what extent on learning with understanding.

However,even now,understanding is not regarded as important always by the designers of curriculum and instruction.

2.2.Misunderstanding about “Examination”

Teachers usually believe that a good score means good understanding.We argue that:this hypothesis is right only when the test has good validity and reliability.Tests of knowledge reproduction level cannot evaluate mature understanding.Our test paper is filled up with questions focus on recognizing and memorizing knowledge.For example,“What's the boiling point of water under standard atmospheric conditions?”“What are the differences in functions between arteries and veins？”“What is ‘density’”? “What is migration?”...

These questions can only reach the goals of testing the ability of memory level and superficial understanding.It is easy for students pass the exam by memorizing the concepts.For example,the researcher once did an experiment:I asked primary students why our human being will not fall into the universe.They said that it is because of the gravitation of the earth.Then I asked them to draw a picture about the people on the earth,most of them draw like this.

The picture indicates that students do not really believe gravitation.They still think that the reason why our human beings will not fall into the universe is the earth is holding us.It suggests that understanding does not mean memorize knowledge and a succession of correct answer.As Novak(1998)argues,it is difficult to nose out the successful performances on creating,leaning and employing.As the traditional evaluation system only focuses on evaluating the knowledge of subject and with measures of quantization.Norwak asserts that:“The inappropriate way of evaluating in elementary schools and middle schools (including colleges and universities) is absolutely barriers to progress on understanding.”(Minizes et al.,1999)[10]

To be fair,educators and researchers have made strenuous efforts on evaluating understanding.Typically,Bloom is one of the outstanding one in this field.But with the further comprehension on understanding,more and more effective tools and ideas are in the development.To evaluate understanding is under research.There is promising future on evaluation tools developed by some international academic organization.Here is one example.

Science test in PISA2006——Evolution

Problem:

Most horses today are streamlined and can run fast.Scientists have found the fossil skeleton of animals that are similar to horses.They consider them to be the ancestors of the present-day horse.The scientists have also been able to determine the period during which the fossil species were living.

The table below provides information on three of these fossils and on the present-day horse.

Q1:what information in the table is strong evidence that present-day horses may have evolved over time from the other three animals?

Q2:What further research can scientists undertake to find out how horses have evolved over time?

Circle “Yes” or “No” for each of these statements.

Q3:Which one of the following statements best applies to the scientific theory of evolution?

A.The theory cannot be believed because it is not possible to see species changing.

B.The theory of evolution is possible for animals but cannot be applied to humans.

C.Evolution is a scientific theory that is currently based on extensive evidence.

D.Evolution is a theory that has been proven to be true by scientific experiments.

Obviously,it is difficult to answer these questions without deep understanding on evolution.

If we want to promote teaching for deep understanding in China,we should try to construct the evaluation system first.

2.3.Learning the important core concept too fast for the students to understand

Concept and theory are the kernel of any subject.The importance of them will be mentioned in the following part.This kind of knowledge is different from statement knowledge,they have characters of eternity,universality,abstraction and generalization.Compared with the statement knowledge which can be learned through demonstration and lecture,the concept and theory can only be grasped by deep engagement,experiment and thinking hard abstract thinking.Since learning of them is not only knowing the meaning of words,but also gaining the way of think about the concepts,without this,it may be mired in a doctrine.For example,we want to understand a concept such as “system”.We cannot only know the definition of “system”.As it is not deep understanding of “system” if we cannot employ systematic thinking.

Concept itself and the way of thinking related to which are the surface layer of the same thing,and it will be more difficult and take more time to gain the latter.Piaget argues that understanding is discovery...Child will keep the knowledge if he/she gain them through unrestricted survey and voluntary hard working.And he/she will learn some methodology and benefit from it in a lifetime with the interesting to study.At least,doing this can avoid neglecting the rational thinking and overemphasizing the cramming for test...The purpose of intellectual education is not repeating and learning the facts already existed,but learning the facts by themselves.It is inevitable of wasting time because of choosing the wrong way (quoted in Feden ＆ Vogel,2002).[11]

Unfortunately,it is too often that teachers are lack of enough patience on putting emphasis on students' deep understanding and dislike to devote more time for it.Most of them believe in “speaking pithier and practicing more”.The practicing here means a large amount of exercises instead of cultivating students' ability of thought and practice on constructing knowledge.It might be named as “linear teaching”,in which students neither spend time on understanding the kernel concepts,nor applying use those concepts in flexible ways.

Oppositely,there is a parabolic teaching,which is a kind of student centered teaching.At the beginning,progress is slow:teachers should perceive the prior concept,challenge to the problematic those prior concept,make students realize where the problem is and then construct new concept...This kind of teaching progresses slow at the beginning,but it is sufficient for students to grasp the kernel concept and result in fast steps on the following teaching progress.Parabolic teaching focuses on “quality is more important than the quantity”,“understanding is more important than remembering and feeling”,could we gain some inspiration from this and add something new to the mode of “speaking pithier and practicing more”?

2.4.The content of course is too miscellaneous to develop deep learning

The following prospects show how the course influences deep learning.

2.4.1.Core concepts are submerged by details

There are lots of facts in each subject,and there are some core concepts in each subject,the following table shows the core concepts in different subjects.[12]

Examples of core concepts in different subjects

The traditional way of curriculum design model is list a lot of themes and facts without emphasis on the main concepts and principles.The core concepts get lost in substantive trivial(or there is not core concept in the mind of the curriculum designers).Too much information may disturb deep learning of the students.For example,students may learnt many things about peasants uprising,and they remember them,but if they did not notice the relationship of those facts with the core concept “conflict”,students were still not able to analyze the reason of other peasants uprising;too many details may cost too much time and students have few opportunities to think about the core concept.

2.4.2.Textbooks are too brief to be understood by students

It is not clear the reason that content of textbooks for Chinese students are concise due to the consideration on scientific perspectives or reduction of publishing cost.Compared with textbooks abroad,the words in Chinese textbooks are really succinct.Those important concepts are briefly introduced only.Let's make a comparison about the following two examples.

·The quality of substance with a unit of cubage is named density of substance.The formula is:ρ= m / V。

·Initiative transportation:If you have ever ridden a bike down the mountain,you must know that you can ride fast without much energy,but it is difficult to be back to the mountaintop.To cells,by diffusing and sinking just like riding down the mountain,no energy would be cost.Passive transportation is a kind of transportation which makes substance through membrane without cost any energy.[13]

The first example is brief,but it seems to be lack of examples,it is adverse to self-studying or understanding. The second example seems has the fault at excess wordage,but it links with students' experiences of riding a bike,employing the similarity of both of riding a bike down the mountain and sinking cost no energy,therefore,it could help the students understand correlative knowledge.

2.4.3.Expressing core concept in definitive ways

Since it is impossible to grasp the core concept in one move,thus the designers of courses should not express them in definitive ways.However,it seems to have many problems of this kind in our textbooks.The main problem is that students are pumped into much concepts and deprived of opportunities of constructimg knowledge.Here are some examples.

The experiment aims to fostering students' inquiring ability through understand the external condition of seed germination.The experimental procedures,including choosing seeds,setting experimental object and control object,originally should be designed by students rather than the designer of the textbook.Obviously,the opportunities of proposing hypotheses,designing the experiment and proving the findings are deprived,that means students miss the opportunity to practice their thought and have deep understanding.

However,it is not every piece of knowledge needs to be understood deeply,it just take place in a tiny part of one subject.Wiggins and McTighe (1998) propose a graph showing the levels of the content of course using optimization procedure,they assert that the smallest round should be the key point of the class,students should have eternal understanding—understand the parenchyma or spirit of those important concepts[14].

Only a few parts of the content of the curriculum that should be permanently understood is appropriate to use parabolic way of learning,it is advisable to consider the forms of expression as to do the least possible the definitive ways.Otherwise,students will not enjoy the moment of illumination of deep understanding,as genuine understanding links thought and feeling,mind and body with an “aha!” in their insight.

The other factor of curriculum obstacles the deep understanding,namely as de-contextualization will be mentioned in next part.

3.Treatments of “fragile knowledge syndrome”

The key to cure “fragile knowledge syndrome” is to promote deep understanding.However,it is hard to change the situation only focus on the teaching.The treatment of fragile knowledge syndrome is a systematic engineering which should be started based on multi-dimension and perspectives.

3.1.Following out the principle of “less is more” in curriculum design

Firstly,we should adhere to one principle:the quality of knowledge is much more important than the quantity.

The philosophy of curriculum design should turn from “a width of one mile and a depth of one inch” to “a width of one inch and a depth of one mile”.This idea of the new curriculum is not at all expedient to response “Knowledge explosion”,particularly,is a new idea of curriculum design:the priority selection should be the top of the pyramid of knowledge,namely principles,generalization concepts,rules and theories (Erickson,2002) [15].

We name these kind of knowledge as core concept.It is defined as those declarative knowledge,are required to be remembered and understood by teachers and still could be applied after having forgotten all of the non-essence information.Although to some extent,the core concept is the kernel of some knowledge;not everyone can accept this kind of knowledge,but they have been used a lot and it holds during a long period.

There are not many core concepts in each subject,but they are very important.The core concept is important in that it could be transferred.Therefore,students could think go beyond the topics and facts.For instance,if students understand the essence of war,not only can they understand how the war occurs,how to avoid the war,but also bring them the methods of analyzing wars in the past and the future,even how to look on the conflicts in our daily life which can be viewed as “Micro-wars”.

Secondly,we should pay more attention to the connection between facts and core concepts.

Paying more attention to core concepts doesn't mean ignoring learning of facts.Oppositely,we should preserve and employ those facts that are of great importance to understand core concepts.Otherwise,learning of abstract knowledge would be a tree without roots and water without a source.However,facts-learning should not be the purpose,but the assistant of understanding concept.When learning the facts,we should focus on the connection with the core concepts.The right way is that centralizing the deep conceptual knowledge and developing the comprehensive ability based on the facts and develop understanding with the help of facts.For example,if we look at the American Revolution,then we can define transferable lessons of history that students can apply in their future study through the conceptual lens of dependence/independence.

·Economic need can create a dependence of one nation upon another.

·Social,economic,or political oppression often leads to conflict or revolution.

·A nation's desire for political or economic freedom and independence may facilitate alliances with other nations (Erickson,2002).

Thirdly,core concept should not be expressed in the form of direct answer.

Since we can't get deep understanding in a short time,we can get it through processing the information that are meaningful for individuals during the period of cooperating with others,then we should not express core concept in the textbooks in a direct way.“Clever” students won't find the facts themselves if they have already known the conclusion.So,teachers,in writing curricula,need to identify conceptual ideas,often stated as essential understandings,which are developmentally appropriate for the age level of their students.Therefore,in curriculum design and instruction,a major task is to address clearly the key concepts and generalizations,which is prioritized related to the critical content of our disciplines.The endeavor on curriculum designing is gathering momentum and is there to stay since 1950s.

3.2.Turn teaching place to learning place

There is no intention of weighing two acts of extreme instruction:lecturing and inquiring.Instead,as the saying goes,“there are certain regulars in teaching but no hard and last rules one can follow in order to teach perfectly”.The parabolic learning method should be employed on learning of core concept and making the process slowly,surely and deeper.Since the key point of developing the students' realization and deep understanding is to make them engage in the learning activities.Only when engaging in the learning activities,can the students gain the feeling of knowing the connection naturally but difficult to express.An insight,an “aha...” is a gestalt.It is the coming together of thoughts and ideas and senses and impressions and emotions,deep understand links thought and feeling,mind and body.(Erickson,2002)[16]

Chinese educators have similar feeling in this point,and put forward directly.The result won't be bad if the process is good;if the students are initiative,the result will be better.A set of teaching modes aimed at promoting deep understanding emerged because of demand.For example,3E learning circle,project-based learning,problem based learning and so on.They have really similarities in common with educational faith[17].

1.Knowledge is constructed by the learners themselves.

2.Learning of new knowledge will be effected a lot by the existing knowledge.

3.Teachers should be the manager of a supermarket of building materials,who provides students all kinds of building materials and help them design,then let the students build the houses on their own.Teachers should not be brokers of real estate who build the house first and then sell it to the students.

4.Learning in context.Core concepts should be in context and be handled by the students.

5.Learning is not an individual activity but a social activity.The following examples which illustrate the idea come from the class of math,Chinese literature and English.

(1)Teaching of Bernoulli's law (3E learning circle)[18]

(2)Non-directional method of writing essay[19]——《My self-painting》

·Who are they?

A is______________reason __________________________________________

B is______________reason __________________________________________

From this,we can tell that you describe a person from prospects.

What other prospects can we use? If you can't find any,you can talk with your partner.

·Look at the following paragraph and guess whom they are.What do you think about the description? Point out the good prospect and revise it if you think it is not that good.

He has curly hair and a horse face.He often narrows his eyes and opens his mouth when he is smiling.He often says “Yeah” and makes a “V” gesture.He is a very famous host.Who is he?

He has a middling stature and likes to act as a geezer:wear a hat under his creasy forehead,walk bumpily with his knees bendy and always with his hands behind his body.He often makes us laugh.Father and I like him very much.

·comparison:What are the differences between describing a person with writing and painting? You can discuss with your friends.Which method do you think is better?

·who is the person I write?

According to the summaries above,describe a teacher who you are familiar with.Then share your writing with the class or your group and let them guess who the person you write is.If they can give the right answer immediately,you succeed.

(3)The format of calculating the cubage of cylinder

At the beginning of the math class,teacher hands out some straight tubs to the students and said:“We have already learned the format of calculating the area of round,the cubage of cube.We are going to learn the format of calculating the cubage of cylinder,and I want you find it out yourself.”

At first,students just thought about filling up the content with water first while have no idea about how to calculate the cubage of cylinder.Then they calm down can recall the words of the teacher:“you have already learnt the format of calculating the cubage of cube...then length multiple width multiple height,what is length multiple width？It is the area of round! We have already know how to calculate the area of the round,then the area of the round multiple height is the cubage of cube,how to prove it? ”The most important thought appears:using the smallest tub as measure and put the same amount of water into each tub,then the underside area of the container multiple the height of water,if the results are the same or similar,we can prove the idea is right...

This experiment shows that students' understandings to Bernoulli's law,grappling the main characters of people to write and the formula of the cubage of cylinder are mature and profound.Teachers who emphasize understanding often ask themselves this question:how can I help the students join in to make sure we can get a conclusion?

3.3.Design of learning core concept in contexts

Design of learning core concept in context has two meanings.Firstly,it is that learning core concept should be connected with the experience of children closely.Secondly,it is that learning core concept should be connected with the real world.The first one is supposed to solve the problem of making the content of the course be meaningful,the latter one is supposed to solve the problem of the connection between direct experience and indirect experience.

We usually heard the children complaining.Why should I learn this? What benefits can I get from this class?...Actually,if the content of course is away from the experience of the students or their lives,it will become a heavy burden to the students since it is meaningless to them.It is good that the problems in this prospect have already been noticed by educators,we can find it out through the changing of textbooks and the teaching design of teachers:“Measure the perimeter of your fist and the length of your feet,what can you find? How to buy a suitable socks with the help of your finding?”“In this experiment,you need to compare the effects of two different kinds of disinfector.”When teaching Newton's first law,at the beginning the teacher ask:people who sit on front seats have to must fasten seat belt? Connecting to children's experience and life have become the motto of curricular designing.

Because of the characters of children's cognition,we emphasis on connecting to the real world in school.What mainly children learn in school mainly are symbols.The knowledge had been inherited from ancestors and learning of it is very important.But knowledge represented by symbols is abstract and hard to understanding because it is divorced from its culture and contexts.If we don't teach it in special contexts,students would have difficulties in understanding how does this knowledge generate and how to use it.So,Dewey claimed that concept,skill and believe will be meaningful and useful only in contexts(Dewey,1938)[20].Besides,we find this teaching method have other advantages:children are glad to learn and they construct things by themselves.Children learn foreign language well in the contexts of using the language,which prove that contexts are very important to learning.We should note that we are not repeating Dewey's ideas.Learning of core concept in contexts absorbs the advantages of Dewey's and Bruner's theories.Its exact description is:if want valuable and meaningful learning happen,students must learn in a special context,even the content they learn is prescriptive,standard,appointed and determined by outside.

We must be careful of walk to the other extremity when emphasize on learning core concept in contexts:simply think that learning in context equal to community practice,visit,interview and other activities.Don't forget“learning in context”also need concept,skill and belief to make experience to be understanding(Dewey,1915)[21].There are lots of education resources in the real world.But they are latent and cannot be discovered unless teachers focus on them.Take a pond for example,in students' view,a pond is a environment filled with water,and plankton.However,there are many latent elements of math,say,dimensions,perimeter,diameter,cubage and so on in math teacher's eyes.Similarly,there are other latent elements of zoology and aesthetics.The real relations cannot be automatically revealed unless curriculum designers and teachers lead to that way.

3.4.Evaluation of facilitating understanding

“Teaching follow examinations” may be the oldest apothegm in the area of education.So the constructing the evaluation of understanding is the main treatment to “fragile knowledge syndrome”.The key question of constructing the evaluation of understanding is how to guarantee that people cannot pass exams only by remembering the definition without understanding .

We can get some advice from the standard of evaluating understanding.

Bloom argued that we can evaluate understanding through explanation,translation and deduction.Explanation is rational demonstration and illumination of things which often deal with knowledge about “why”and “how”.For example,“why do all of the falling objects have the same acceleration?”Translation is meaningful interpretation,narration and version.Typically,“give some examples”,“tell us with your way”are useful methods for testing translation employed by Chinese teachers.Translation also includes the ability of transferring knowledge from one form to another form.Deduction means predicting or setting up the cause and effect connection among the things based on the learnt knowledge.For example,calculate the height and location of light source according to the object and shadow (Bloom,1956)[22].Bloom's idea has been widely used in the evaluation system of examinations in China.

The four dimension on understanding proposed by researchers in Harvard University may provide us with some new inspiration.

(1)Evaluate understanding from the connection of knowledge

The integrated and rich concept maps are regarded as key criteria for evaluating on understanding.According to this idea,concept maps could be used as evaluation tool.It is a visual external representation of the connection between concepts.It demonstrates the relationship between concepts in integrate and intuitive way,and makes it convenient to evaluate the property of knowledge used in the tests.Graphs below are constructed by two students and it shows the differences of understanding on magnet.

(2)Evaluate understanding based on application of methods

This dimension focuses on the “syntactic structures” of knowledge,that is the understanding of knowledge.Researchers of Harvard argue that students' understanding of knowledge should include understanding of methods.According to application of research methods,students may question the statements or construct new knowledge.This viewpoint gives us inspirations about evaluation.In recent year,this kind of questions appear in the exams in China.For example:three students inquire which can shield the remote signal best using paper,plastic film and cotton cloth at home.Student A does this experiment at his home.He put several pieces of paper between the remote and TV,operates the remote and if it still can influence the TV,increases the number of pieces of paper until the remote can't control the TV.He mark down the number of the paper— 14 pieces.Student B does the same experiment but use plastic film at her home.She mark down the number of the plastic film—20 pieces .Student C does the same experiment but use cotton cloth at his home.He mark down the number of the cotton cloth— 10 pieces.They draw the conclusion:cotton cloth can shield the remote signal most effectively among paper,plastic film and cotton cloth.The inquiry questions are:

(a) these three students made some mistakes during the process of exploring,please point out the errors they made;

(b)select an error and explain how to correct it.

These two questions can evaluate students' understanding about the inquiry learning methods effectively.

(3)Evaluate understanding from the application of knowledge

Application means applying the knowledge we learned in a new environment,such as employing economic knowledge to design a finance project of investment and saving.

(4)Evaluate understanding from various of forms of expression

It focuses on understanding a variety of representation of knowledge.We can use it in reverse,using various forms of expression to evaluate students' understanding.

Picture 1

Picture 2

In picture 1,someone with a ball in hand stands in three different positions on the earth.If he drops the ball,please draw the direction of the falling ball with arrows.

In picture 2,open the lid of the bottle,where would the water flow to? Please draw the direction of the falling water with arrows.

“Teaching for Understanding” have become the new slogan in the field of education.It's the recipes to cure “fragile knowledge syndrome”,and we are expecting that this idea could be widely accepted and implemented in Chinese education community.

[1] Perkins,D., Smart Schools:Better thinking and learning for every child,New York:The Free Press,1992

[2] Feden,D.P.＆ Vogel,M.R.,Methods of Teaching:Applying cognitive science promote student learning,NY:McGraw-Hill College,2002

[3] Krajcik,S.J.,Czerniak,M.C.and Berger,C.Teaching Science in Elementary and Middle School Classrooms:A Project-based approach,NY:McGraw-Hill College,2002

[5] Ausubel,D.Theory and Problems of Child Development,CA:Grune ＆ Stratton,1967

[6] Bloom,B.S.Taxonomy of Educational Objectives:The classification of educational goals,CA:Susan Fauer Company,Inc.;Krathwohl,D.R.,Bloom,B.S,1956 and Masia,B.B.Taxononmy of Educational Objectives,Handbook II:The affective domain,CA:Susan Fauer Company,Inc.,1964

[7] Hammond,K.R,Todd,F.J,Wilkins,M,＆ Mitchell,T.O.Cognitive conflict between persons:Application of the “lens model” paradigm,Journal of Experimental Social Psychology,No.2,1966

[8] Perkins,D.Teaching for Understanding:Linking Research with Practice,NY:Jossey Bass Education,2002

[9] National Science Education Standards,Washington,DC:National Academy Press,1996

[10] Minizes,J.J.Wandersee,H.J.and Novak,D.J.(1999) Assessing Science Understanding:A human constructivist view,London:Elsevier Academic Press

[11] Feden,D.P.＆ Vogel,M.R.Methods of Teaching:Applying cognitive science promote student learning,NY:McGraw-Hill College,2002

[12] Erickson,H.L,Concept-based Curriculum and Instruction:Teaching beyond the facts,London:Sage,2002

[13] Pedilla,J.M.,Miaoulis,L.＆ Cyr,M.,Science Explorer:Cells and heredity,NY:Prentice Hall,2000

[14] Wiggins,G.＆ McTighe,J.,Understanding by Design,VA:Association for Supervision and Curriculum Development,1998

[15] Erickson,H.L,Concept-based Curriculum and Instruction:Teaching beyond the facts,London:Sage,2002

[16] Erickson,H.L,Concept-based Curriculum and Instruction:Teaching beyond the facts,London:Sage,2002

[17] Feden,D.P.＆ Vogel,M.R., Methods of Teaching:Applying cognitive science promote student learning,NY:McGraw-Hill College,2002

[18] This case is adapted from designs by Professor Li,Yingtian,Normal University in Taipei.

[19] These cases come from School of teachers development,Qinye Community,Changzhou.

[20] Dewey,J.,Experience and Education,Indianapolis:Kappa Delta Pi,1938/1998

[21] Dewey,J.,The school and Society,Chicago:The University of Chicago Press,1915

[22] Bloom,B.S.,Taxonomy of Educational Objectives:The classification of educational goals,CA:Susan Fauer Company,Inc,1956