G.Polya and“How to Solve It!”An overall framework for problem solving was described by G.Polya in a book called“How to Solve It!”(2nd Ed.,Princeton University Press).Although Polya’s focus was on solving math problems,the strategies are much more general and are broadly applicable.Inductive reasoning is the basis of most of the creative processes in the“real world”.Physics provides an ideal laboratory for building skill in inductive reasoning and discovery.Here is an outline of Polya’s framework:1.Understand the Problem[Identify the goal]Thefirst step is to read the problem and make sure that you understand it clearly.Ask yourself the following questions:•What are the unknowns?•What are the given quantities?•What are the given conditions?•Are there any constraints?For many problems it is useful to•draw a diagramand identify the given and required quantities on the ually it is necessary to •introduce suitable notationIn choosing symbols for the unknown quantities we often use letters such as a,b,c,x,and y,but in most cases it helps to use initials as suggestive symbols,for instance,V for volume or t for time.2.Devise a PlanFind a connection between the given information and the unknown that will enable you to calculate the unknown.It often helps you to ask yourself explicitly:”How can I relate the given to the unknown?”If you do not see a connection immediately,the following ideas may be helpful in devising a plan.•Establish subgoals(divide into subproblems)In a complex problem it is often useful to set subgoals.If we canfirst reach these subgoals,thenwe may be able to build on them to reach ourfinal goal.•Try to recognize something familiarRelate the given situation to previous knowledge.Look at the unknown and try to recall a morefamiliar problem that has a similar unknown or involves similar principles.•Try to recognize patternsSome problems are solved by recognizing that some kind of pattern is occurring.The patterncould be geometric,or numerical,or algebraic.If you can see regularity or repetition in a problem,you might be able to guess what the continuing pattern is and then prove it.[This is one reasonyou need to do lots of problems,so that you develop a base of patterns!]•Use analogyTry to think of an analogous problem,that is,a similar problem,a related problem,but one that iseasier than the original problem.If you can solve the similar,simpler problem,then it might giveyou the clues you need to solve the original,more difficult problem.For instance,if the problem isin three-dimensional geometry,you could look for a similar problem in two-dimensional geometry.Or if the problem you start with is a general one,you couldfirst try a special case.[One must domany problems to build a database of analogies!]1•Introduce something extraIt may sometimes be necessary to introduce something new,an auxiliary aid,to help make theconnection between the given and the unknown.For instance,in a problem where a diagram isuseful the auziliary aid could be a new line drawn in a diagram.In a more algebraic problem itcould be a new unknown that is related to the original unknown.•Take casesWe may sometimes have to split a problem into several cases and give a different solution for eachof the cases.For instance,we often have to use this strategy in dealing with absolute value.•Work backward(assume the answer)It is often useful to imagine that your problem is solved and work backward,step by step,untilyou arrive at the given data.Then you may be able to reverse your steps and thereby constructa solution to the original problem.This procedure is commonly used in solving equations.Forinstance,in solving the equation3x−5=7,we suppose that x is a number that satisfies3x−5=7and work backward.We add5to each side of the equation and then divide each side by3to getx=4.Since each of these steps can be reversed,we have solved the problem.•Indirect reasoningSometimes it is appropriate to attack a problem indirectly.In using proof by contradiction toprove that P implies Q we assume that P is true and Q is false and try to see why this cannothappen.3.Carry out the PlanIn step2a plan was devised.In carrying out that plan we have to check each stage of the plan and write the details that prove that each stage is correct.A string of equations is not enough!4.Look BackBe critical of your result;look forflaws in your solutions(e.g.,inconsistencies or ambiguities or incorrect steps).Be your own toughest critic!Can you check the result?Checklist of checks:•Is there an alternate method that can yield at least a partial answer?•Try the same approach for some similar but simpler problem.•Check units(always,always,always!).•If there is a numerical answer,is the order of magnitude correct or reasonable?•Trends.Does the answer vary as you expect if you vary one or more parameters?For example,if gravity is involved,does the answer change as expected if you vary g?•Check limiting cases where the answer is easy or known.Take the limit as variables or parametersreach certain values.For example,take a mass to be zero or infinite.•Check special cases where the answer is easy or known.This might be a special angle(0or45or90degrees)or the case when all masses are set equal to each other.•Use symmetry.Does your answer reflect any symmetries of the physical situation?•If possible,do a simple experiment to see if your answer makes sense.We will examine potential strategies as we solve problems.The emphasis here is on being conscious of our problem-solving strategies and on constructing a solution that reflects the steps outlined above.2。
教案课程名称：内科学心血管病本课内容：总论授课对象：口腔医学专业本科生授课时间：45分钟授课教师：曹月娟一、教学目的通过学习内科学心血管疾病总论，使学生掌握循环系统的定义，了解心血管疾病流行病学特点、掌握心血管病的分类，熟悉当前心血管病诊断方法和治疗手段，了解心血管病的研究进展。
二、教学内容1.循环系统定义和循环系统疾病2.心血管病与人口死亡率3.心血管病的分类4.心血管病的诊断5.心血管病的预后6.心血管病的防治7.心血管病研究进展三、教学重点本节课教学的重点有两个：①心血管病的分类；②心血管病的诊疗方法。
掌握心血管疾病的分类是进一步学习和研究心血管疾病的理论基础。
在教材内容的基础上增加病例举例，对心血管病分类加以诠释；对于当前心血管病的诊疗手段进行举例说明，使学生对抽象的概念有更直观的认识，能较好的理解加深记忆。
四、教学难点本节课教学的难点是心血管病的诊断治疗，也是本节课教学的重点，所以对于每一中诊疗手段的讲解，除了对教材上知识的详尽讲述外，还特别举实例加以说明，帮助学生更深刻的理解心血管疾病的诊断和治疗方法。
五、教学方式板书和多媒体相结合、教师讲解和学生课堂讨论相结合。
六、教学创新模式1.教学内容在详细讲解教材基本理论的基础上，不仅仅局限于书本内容，查阅大量相关资料，增加信息量，扩大学生的知识视野。
在讲解过程中，使理论与实际相结合，向学生介绍心血管疾病应用的各种诊断手段和不同治疗措施，枚举经典实例，使学生意识到所学的知识具有重要的应用价值，从而提高学习的积极性和主动性。
在学生能够理解的前提下，适当介绍国内外相关领域的最新研究动态，并推荐相关的专业性网站，便于学生随时浏览，使学生了解一些学术前沿的知识。
2.教学方式采取板书和PPT结合的教学方式，PPT具有直观性和快捷性，利用多媒体展示重要的概念、直观图片和影像资料。
同时在教学过程中板书列出一些专业英文词汇，便于学生阅读英文专业文献，获得最新、最好专业知识，也为以后的双语教学打下基础。
C P C循环(C P C c y c l e)：“详察(circumspection)-预断(preemption)-控制(control)循环”的简称。
个体遇到新情境时的行为特征。
美国心理学家G.A.凯利提出。
他认为个体遇到新情境时，行为表现为三个(1)详察期，个体总是谨慎地尝试多种前提构念，提出各种命题构念，这些构念只是对情境的可能的解释。
(2)预断期，从上一阶段经过权衡的各种构念中选取可供决断的构念。
(3)控制期，在可供选择的构念中评价出最有效的构念并作出选择。
CPC循环是个体适应社会生活的重要过程。
感觉圈(sensory circle)：亦称“触觉圈”。
皮肤上两个触点被感知为一个的区域。
德国生理学家韦伯1834年首次提出。
其大小随身体的不同部分而改变。
后发展为心理物理学中一个重要假设和实验方法，即两点阈限问题。
人差方程(personal equation)：亦称“个人方程”。
早期反应时研究中反映两个天文观察者个体差异的等式。
与人的神经系统、感觉器官的差别有关。
起因为1796年，英国格林尼治天文台台长马斯基林(N e v i l Maskelyne,1732—1811)发现在观察星辰经过天文望远镜的铜线时，他的助手金尼布鲁克(D.Kinnebrook)总比他记录的时间慢0.8秒。
当时认定助手不负责任，不称职，于是就把他解雇了。
20年后，此事通过《天文学报》公布于世。
德国天文学家贝塞尔(Friedrich Wilhelm Bessel,1784—1846)通过反复研究，发现他与另一位天文学家阿格兰德(Argelander,1799—1875)之间观察同一天文现象的反应时之差是一个常数，即B-A=-1.222秒，A、B分别是两人的反应时。
从而确定人与人的时间差异是客观存在的。
此事为实验心理学中反应时间的研究奠定了基础。
无意识推理(unconscious inference)：德国生理学家亥姆霍兹1855年提出的概念。
