2.3: How is Plato a philosophical leader in education?
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By Laira Stewart
Learning Objectives
- Readers should be able to define the Socratic method
- Readers should be able to give an example of the dialectic method
- Readers should be able to describe Plato’s educational thought as outlined in The Republic
Overview of Plato
Considered by historians to be one of the most influential minds of Western thought, Plato described the Socratic method of instruction and further developed this dialectic method in his later years. (Smith, 1997). The Socratic method is basically a learning method using a question and answer dialogue between the teacher and student. The idea is that the ensuing debate exposes flaws in reasoning and brings forth a better understanding of the issue. Plato improved on the Socratic method in his later years and developed a philosophy of education as outlined in The Republic that became the hallmark of a European liberal arts education.
427 to 347 BC. Plato was born in Athens in 427BC. When his father died, his mother married, Pyrilampes, a friend of Pericles. Plato began to pursue a political career, but became disillusioned with the politics of the time. Evidently, he was good at athletics, poetry and drama. In 409 BC he met Socrates, and according to Plato, he was one of Socrates more outstanding students. Socrates did not follow the then current trend of the Sophist method of teaching which used rhetoric or persuasion to dictate learning to their students. The Sophists asked high fees for their teaching while Socrates charged nothing. Plato, while mistrustful of the Sophists did share their interest in investigating values rather than physical science. In 399 Socrates was brought to trial for corrupting the minds of youth because of his skepticism regarding religious deities. He was convicted and sentenced to death. Socrates committed suicide rather than face execution. Plato wrote about the trial and Socrates decision not to try to escape from prison. After this Plato traveled extensively studying religion, geometry and astronomy. In 387 BC he returned to Athens and founded a university that included philosophy, physical science, astronomy and mathematics. Plato also developed a philosophy of education for prospective rulers requiring them to be philosophers first and rulers second as detailed in The Republic He is thought to have died at the age of 80 in 347 BC. (GradeSaver).
Socratic Method
The Socratic method is a dialectic method of teaching, named after the Greek philosopher Socrates, in which the teacher uses questions to get the student to think about what he/she already knows and to realize what they do not know. This question and answer session stimulates the brain, engages the learner, and can bring new ideas to life. As one educator stated, “Think of it as the relentless pursuit of truth through unceasing questions. To engage in dialectic method, establish your goal to clearly understand truth and get on with it.” (Kern, 2008).
Today, law schools are trying to find better ways to teach their students the important concepts they will need in the future. The Socratic Method is one of the ways a lot of teachers have found to be most useful. Since the Socratic Method is the basis for which courts handle cases, it seems only fitting to have the students at a law school learn that way. In a court room a series of questions are asked to get the judge and/or jury to see the truth of the situation at hand. The teacher likes using the Socratic Method in their classes because they believe it helps the students get into the mind set of being a lawyer, plus they believe it helps the students learn and retain the information better. "One of the principle benefits that the Socratic Method confers is to allow large bodies of students to engage in "active learning." "Students learn better when they are actively involved in the learning process" rather than passively taking notes and the teacher dispenses information." (Jackson, 2007).
Note
Here are some Videos on Plato
These links will take you to some very interesting videos about Plato and Socrates.
1.
Watch this clip,
Plato
The Encyclopedia Channel. YouTube.
2.
Watch this clip,
Socrates
How Stuff Works.
3.
Watch this clip,
Socratic Method in Law school
Pacific McGeorge School of Law Faculty. YouTube.
Dialectic Method Example
The benefits of this method are that the student becomes engaged in the learning process and contributes in developing the answers (led by the teacher). This is in contrast to didactic learning in which the teacher tells the student what they need to know.
Begin with a question that has several possible answers or is ambiguous so that you can begin asking the question in different ways until the students reason out the answer you wish them to learn. Then encourage them to ask themselves other responses.
For example: High School class discussion after reading the Noah’s Ark story from the Old Testament:
Teacher: What is a covenant?
Possible answer: An agreement.
Teacher: I agree to meet you for lunch, is that a covenant?
Possible answer: Sort of.
Teacher: What was the covenant God made to Noah?

Teacher: Does a covenant imply something more than an agreement?
Possible answer: A promise
Teacher: Yes, a covenant is an agreement with a promise. I make an agreement to meet you for lunch and I promise to be there no matter what.
Notice in this example the student has come up with the answer. If the teacher had simply told the student the definition of a covenant, chances are the student would simply not care to remember the meaning. In this example, the student is more likely to remember the meaning since he/she was involved in finding the answer.
Note
Go to this link for a specific example that was used in a 3rd grade elementary math class.
Thoughts on the Republic
Plato believed that a teacher must care deeply for the student and have a good understanding of the subject being taught. In The Republic Plato outlines a lifelong learning process for rulers that begins with learning to read, write and do mathematics at age six. As the child grows music and sports are added. At age 18 military services are added. At age 30 the ruler should study philosophy and politics. It is not until age 50 that the ruler should rule. This lifelong liberal arts education would ensure that the ruler had experience and wisdom in order to make just decisions. The Republic is mostly about defining justice and the different types of justice. Only a philosopher-King can dispense the appropriate justice. This method of instruction became useful during the Middle Ages in the royal classes, and can be seen in the British royal family today. The British males are required to do military service, attend university, and work in civil service for many years before they take over the role of King. An interesting note is that the current Queen of England, Elizabeth, was reluctant to hand over the reins to Phillip until after he had a wife and family, and has not yet retired. (Jowett)
Note
Here are some other interesting links on Plato
These links will take you to some very interesting videos about Plato and Socrates.
1.
Click this link,
Plato Biography
Kraut.
2.
Click this link,
Plato Outline
Kemerling.
3.
Click this link,
Socratic Method in Law Schools
Jackson.
Summary
Both the Didactic and Dialectic methods are necessary for teaching. There are many times when telling the student what he/she needs to know is the only way to impart information. However, the dialectic method is essential for engaging students in interactive learning, in giving them some ownership of discovery in the learning process. The dialectic method can provide an opportunity for debate of issues, exploration of ideas and use of higher thinking skills. Since the object of learning is to be able to discern and make decisions based on knowledge, the dialectic method is critical for growth of knowledge.
References
Anderson, Ronald D. (1994). Issues of Curriculum Reform in Science, Mathematics and Higher Order ...office of research, [Abstract]. US Department of education. Retrieved from http://books.google.com/books?id=hwmb_mqZgVQC&pg=PA44&lpg=PA44&dq=teach+by+asking+instead+of+telling&source=web&ots=WnZ-otfmkT&sig=chknfZ02MSgDTPQj0-oUwTU7XBY&hl=en&sa=X&oi=book_result&resnum=10&ct=result#PPA44,M1
Garlokov, Rick. The Socratic Method:Teaching by Asking Instead of by Telling. Retrieved September 22, 2008, from http://www.garlikov.com/Soc_Meth.html
GradeSaver. Plato. (n.d.) Harvard College. Retrieved October 5, 2008, from http://www.gradesaver.com/classicnotes/authors/about_plato.html
How Stuff Works. A Discovery Company. Ancient Greece: Socrates and Plato. (n.d.) [Video File]. Video posted to http://videos.howstuffworks.com/hsw/25880-ancient-greece-socrates-and-plato-video.htm
Jackson, Jeffrey D. ,Socrates and Langdell. (May 17, 2007). Legal Writg: Is the Socratic Method a Proper Tool for Legal Writg Courses?. California Western Law Review, Vol. 43, No. 2, pp. 267–308, Available at SSRN: http://ssrn.com/abstract=986343
Jowett, Benjamin. The Republic by Plato. Available from http://classics.mit.edu/Plato/republic.html
Kemerling, Garth. (Last updated on 9 August 2006). Plato. Philosophy Pages. Retrieved October 5, 2008, from http://www.philosophypages.com/ph/plat.htm
Kern, Andrew. Two Methods of Instruction. Articles from The Classical Teacher. Retrieved September 22, 2008. www.meuimoriapress.com/articles/twoinstuct.html
Kraut, Richard. (March 20, 2004). Plato. Stanford Encyclopedia of Philosophy. Retrieved October 5, 2008, from http://plato.stanford.edu/entries/plato/
Plato. (n.d.) The Internet Encyclopedia for Philosophy. Retrieved September 22, 2008, from http://www.iep.utm.edu/p/plato.htm
Smith, Mark K. (First published May 8, 1997. Last update: April 11, 2008). Plato. From http://www.infed.org/thinkers/et-plato.htm
University, of Chicago, The Law School. The Socratic Method (n.d.) Retrieved September 22, 2008, from www.law.uchicago.edu/socrates/method.html
YouTube. (July 13, 2008). Plato - Encyclopedia channel. (n.d.) [Video File]. Video posted to http://www.youtube.com/watch?v=1aWK_69ufbo
YouTube. (August 22, 2008). Pacific McGeorge School of Law Faculty on the Socratic Method. (n.d.) [Video File]. Video posted to http://www.youtube.com/watch?v=p9B_zYs_ZhY


1.7: Sir Thomas Malory
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- Bonnie J. Robinson & Laura Getty
- University of North Georgia via University of North Georgia Press
(ca. 1415-1471)
Although there are three different men named Thomas Malory in the same general time period, scholars have (mostly) decided that Sir Thomas Malory of Newbold Revel in Warwickshire is the most probable author of Le Morte d’Arthur. If so, the author led a life that does not necessarily correspond to the knightly values espoused by his work, and the text itself was most likely composed while Malory was in prison. The value of Malory’s work is in part that it is a compilation of every previous Arthurian text that the author could find, including French works that he translated; evidently, he was given access to books while in captivity, and the “knight prisoner” includes requests to pray both for his soul and for his deliverance. In addition to the usual stories of King Arthur and the knights of the Round Table, stories that often were told separately—such as the love of Tristan and Isolde (here called Tristrem and La Beale Isoud), or the quest for the Holy Grail—are incorporated into one long narrative. Whether the author intended the work to be published in one massive volume (as its first publisher, William Caxton, did, subdivided into twenty-one sections, or “books”) or as eight separate volumes (as suggested by its structure in the Winchester manuscript), the stories interconnect and foreshadow future events in a carefully-constructed way. Malory puts his mark on the story in other ways as well. As a knight during the Wars of the Roses, which split England into factions, Malory takes a dim view of the future of knightly behavior; rather than follow a higher code, Arthur’s knights easily slip back into the warrior tradition of valuing blood over all other ties, regardless of guilt or of the consequences of their actions. Doing the right thing is no guarantee of safety. Even during the happiest moments in the story, Malory foreshadows that the end is coming, adding a sense of impending doom. His focus on Lancelot offers additional clues about Malory’s priorities. Although the story begins with the conception and birth of Arthur, it ends not with Arthur’s death, but the death of Lancelot. When Lancelot becomes friends with Tristan, he sees for himself the disaster that follows when a knight falls in love with his lord’s wife, but does not learn the lesson. Lancelot is a worthy knight, but it is his son, Galahad, who will achieve the Holy Grail, since he has the spiritual purity that his father lacks. For all of his strength and nobility, Lancelot’s adultery with Queen Guinevere brings down Arthur’s kingdom. Lancelot’s flaws appear to fascinate Malory, since Malory places this tragic figure at the center of the story, rather than Arthur.
1.17.1 Selections from Le Morte d’Arthur
(also called Le Morte DArthur)
Published in 1485
Book VII
CHAPTER XVIII. How the knight yielded him, and how Beaumains made him to go unto King Arthur’s court, and to cry Sir Launcelot mercy.
Then came there many earls, and barons, and noble knights, and prayed that knight to save his life, and take him to your prisoner. And all they fell upon their knees, and prayed him of mercy, and that he would save his life; and, Sir, they all said, it were fairer of him to take homage and fealty, and let him hold his lands of you than for to slay him; by his death ye shall have none advantage, and his misdeeds that be done may not be undone; and therefore he shall make amends to all parties, and we all will become your men and do you homage and fealty. Fair lords, said Beaumains, wit you well I am full loath to slay this knight, nevertheless he hath done passing ill and shamefully; but insomuch all that he did was at a lady’s request I blame him the less; and so for your sake I will release him that he shall have his life upon this covenant, that he go within the castle, and yield him there to the lady, and if she will forgive and quit him, I will well; with this he make her amends of all the trespass he hath done against her and her lands. And also, when that is done, that ye go unto the court of King Arthur, and there that ye ask Sir Launcelot mercy, and Sir Gawaine, for the evil will ye have had against them. Sir, said the Red Knight of the Red Launds, all this will I do as ye command, and siker assurance and borrows ye shall have. And so then when the assurance was made, he made his homage and fealty, and all those earls and barons with him.
And then the maiden Linet came to Sir Beaumains, and unarmed him and searched his wounds, and stinted his blood, and in likewise she did to the Red Knight of the Red Launds. And there they sojourned ten days in their tents; and the Red Knight made his lords and servants to do all the pleasure that they might unto Sir Beaumains. And so within a while the Red Knight of the Red Launds yede unto the castle, and put him in her grace. And so she received him upon sufficient surety, so all her hurts were well restored of all that she could complain. And then he departed unto the court of King Arthur, and there openly the Red Knight of the Red Launds put him in the mercy of Sir Launcelot and Sir Gawaine, and there he told openly how he was overcome and by whom, and also he told all the battles from the beginning unto the ending. Jesu mercy, said King Arthur and Sir Gawaine, we marvel much of what blood he is come, for he is a noble knight. Have ye no marvel, said Sir Launcelot, for ye shall right well wit that he is come of a full noble blood; and as for his might and hardiness, there be but few now living that is so mighty as he is, and so noble of prowess. It seemeth by you, said King Arthur, that ye know his name, and from whence he is come, and of what blood he is. I suppose I do so, said Launcelot, or else I would not have given him the order of knighthood; but he gave me such charge at that time that I should never discover him until he required me, or else it be known openly by some other.
CHAPTER XIX How Beaumains came to the lady, and when he came to the castle the gates were closed against him, and of the words that the lady said to him.
NOW turn we unto Sir Beaumains that desired of Linet that he might see her sister, his lady. Sir, she said, I would fain ye saw her. Then Sir Beaumains all armed him, and took his horse and his spear, and rode straight unto the castle. And when he came to the gate he found there many men armed, and pulled up the drawbridge and drew the port close.
Then marvelled he why they would not suffer him to enter. And then he looked up to the window; and there he saw the fair Lionesse that said on high: Go thy way, Sir Beaumains, for as yet thou shalt not have wholly my love, unto the time that thou be called one of the number of the worthy knights. And therefore go labour in worship this twelvemonth, and then thou shalt hear new tidings. Alas, fair lady, said Beaumains, I have not deserved that ye should show me this strangeness, and I had weened that I should have right good cheer with you, and unto my power I have deserved thank, and well I am sure I have bought your love with part of the best blood within my body. Fair courteous knight, said Dame Lionesse, be not displeased nor over-hasty; for wit you well your great travail nor good love shall not be lost, for I consider your great travail and labour, your bounty and your goodness as me ought to do. And therefore go on your way, and look that ye be of good comfort, for all shall be for your worship and for the best, and perdy a twelvemonth will soon be done, and trust me, fair knight, I shall be true to you, and never to betray you, but to my death I shall love you and none other. And therewithal she turned her from the window, and Sir Beaumains rode awayward from the castle, making great dole, and so he rode here and there and wist not where he rode, till it was dark night. And then it happened him to come to a poor man’s house, and there he was harboured all that night.
But Sir Beaumains had no rest, but wallowed and writhed for the love of the lady of the castle. And so upon the morrow he took his horse and rode until underne, and then he came to a broad water, and thereby was a great lodge, and there he alighted to sleep and laid his head upon the shield, and betook his horse to the dwarf, and commanded him to watch all night.
Now turn we to the lady of the same castle, that thought much upon Beaumains, and then she called unto her Sir Gringamore her brother, and prayed him in all manner, as he loved her heartily, that he would ride after Sir Beaumains: And ever have ye wait upon him till ye may find him sleeping, for I am sure in his heaviness he will alight down in some place, and lie him down to sleep; and therefore have ye your wait upon him, and in the priviest manner ye can, take his dwarf, and go ye your way with him as fast as ever ye may or Sir Beaumains awake. For my sister Linet telleth me that he can tell of what kindred he is come, and what is his right name. And the meanwhile I and my sister will ride unto your castle to await when ye bring with you the dwarf. And then when ye have brought him unto your castle, I will have him in examination myself. Unto the time that I know what is his right name, and of what kindred he is come, shall I never be merry at my heart. Sister, said Sir Gringamore, all this shall be done after your intent.
And so he rode all the other day and the night till that he found Sir Beaumains lying by a water, and his head upon his shield, for to sleep. And then when he saw Sir Beaumains fast asleep, he came stilly stalking behind the dwarf, and plucked him fast under his arm, and so he rode away with him as fast as ever he might unto his own castle. And this Sir Gringamore’s arms were all black, and that to him longeth. But ever as he rode with the dwarf toward his castle, he cried unto his lord and prayed him of help. And therewith awoke Sir Beaumains, and up he leapt lightly, and saw where Sir Gringamore rode his way with the dwarf, and so Sir Gringamore rode out of his sight.
Book VIII
CHAPTER XX. How King Anguish of Ireland was summoned to come to King Arthur’s court for treason.
Then it fell that Sir Bleoberis and Sir Blamore de Ganis, that were brethren, they had summoned the King Anguish of Ireland for to come to Arthur’s court upon pain of forfeiture of King Arthur’s good grace. And if the King of Ireland came not in, at the day assigned and set, the king should lose his lands. So it happened that at the day assigned, King Arthur neither Sir Launcelot might not be there for to give the judgment, for King Arthur was with Sir Launcelot at the Castle Joyous Garde. And so King Arthur assigned King Carados and the King of Scots to be there that day as judges. So when the kings were at Camelot King Anguish of Ireland was come to know his accusers. Then was there Sir Blamore de Ganis, and appealed the King of Ireland of treason, that he had slain a cousin of his in his court in Ireland by treason. The king was sore abashed of his accusation, for-why he was come at the summons of King Arthur, and or he came at Camelot he wist not wherefore he was sent after. And when the king heard Sir Blamore say his will, he understood well there was none other remedy but for to answer him knightly; for the custom was such in those days, that an any man were appealed of any treason or murder he should fight body for body, or else to find another knight for him. And all manner of murders in those days were called treason.
So when King Anguish understood his accusing he was passing heavy, for he knew Sir Blamore de Ganis that he was a noble knight, and of noble knights come. Then the King of Ireland was simply purveyed of his answer; therefore the judges gave him respite by the third day to give his answer. So the king departed unto his lodging. The meanwhile there came a lady by Sir Tristram’s pavilion making great dole. What aileth you, said Sir Tristram, that ye make such dole? Ah, fair knight, said the lady, I am ashamed unless that some good knight help me; for a great lady of worship sent by me a fair child and a rich, unto Sir Launcelot du Lake, and hereby there met with me a knight, and threw me down from my palfrey, and took away the child from me. Well, my lady, said Sir Tristram, and for my lord Sir Launcelot’s sake I shall get you that child again, or else I shall be beaten for it. And so Sir Tristram took his horse, and asked the lady which way the knight rode; and then she told him. And he rode after him, and within a while he overtook that knight. And then Sir Tristram bade him turn and give again the child.
CHAPTER XXI. How Sir Tristram rescued a child from a knight, and how Gouvernail told him of King Anguish.
The knight turned his horse and made him ready to fight.  And then he yielded him unto Sir Tristram. Then come thy way, said Sir Tristram, and bring the child to the lady again. So he took his horse meekly and rode with Sir Tristram; and then by the way Sir Tristram asked him his name. Then he said, My name is Breuse Saunce Pite. So when he had delivered that child to the lady, he said: Sir, as in this the child is well remedied. Then Sir Tristram let him go again that sore repented him after, for he was a great foe unto many good knights of King Arthur’s court.
Then when Sir Tristram was in his pavilion Gouvernail, his man, came and told him how that King Anguish of Ireland was come thither, and he was put in great distress; and there Gouvernail told Sir Tristram how King Anguish was summoned and appealed of murder. So God me help, said Sir Tristram, these be the best tidings that ever came to me this seven years, for now shall the King of Ireland have need of my help; for I daresay there is no knight in this country that is not of Arthur’s court dare do battle with Sir Blamore de Ganis; and for to win the love of the King of Ireland I will take the battle upon me; and therefore Gouvernail bring me, I charge thee, to the king.
Then Gouvernail went unto King Anguish of Ireland, and saluted him fair. The king welcomed him and asked him what he would. Sir, said Gouvernail, here is a knight near hand that desireth to speak with you: he bade me say he would do you service. What knight is he? said the king. Sir, said he, it is Sir Tristram de Liones, that for your good grace that ye showed him in your lands will reward you in this country. Come on, fellow, said the king, with me anon and show me unto Sir Tristram. So the king took a little hackney and but few fellowship with him, until he came unto Sir Tristram’s pavilion. And when Sir Tristram saw the king he ran unto him and would have holden his stirrup. But the king leapt from his horse lightly, and either halsed other in their arms. My gracious lord, said Sir Tristram, gramercy of your great goodnesses showed unto me in your marches and lands: and at that time I promised you to do you service an ever it lay in my power. And, gentle knight, said the king unto Sir Tristram, now have I great need of you, never had I so great need of no knight’s help. How so, my good lord? said Sir Tristram. I shall tell you, said the king: I am summoned and appealed from my country for the death of a knight that was kin unto the good knight Sir Launcelot; wherefore Sir Blamore de Ganis, brother to Sir Bleoberis hath appealed me to fight with him, outher to find a knight in my stead. And well I wot, said the king, these that are come of King Ban’s blood, as Sir Launcelot and these other, are passing good knights, and hard men for to win in battle as any that I know now living. Sir, said Sir Tristram, for the good lordship ye showed me in Ireland, and for my lady your daughter’s sake, La Beale Isoud, I will take the battle for you upon this condition that ye shall grant me two things: that one is that ye shall swear to me that ye are in the right, that ye were never consenting to the knight’s death; Sir, then said Sir Tristram, when that I have done this battle, if God give me grace that I speed, that ye shall give me a reward, what thing reasonable that I will ask of you. So God me help, said the king, ye shall have whatsomever ye will ask. It is well said, said Sir Tristram.
1.17.2 Reading and Review Questions
1. Both love and duty play important roles in the story. Which one do the characters seem to value more, and why do you think so? Does the author seem to imply one is better than the other?
2. Which knight or knights appear to be loyal to the chivalric code, but not the Christian code? What happens to him/them?
3. Are any of the characters in the story positive role models for the original audience? Why or why not?
4. How does the tone of the story affect your reading of it? If the tone were different (either neutral or more positive), would it change your view of the story? Why or why not?
5. Does anything surprise you about the way that the characters are portrayed? Does anything seem out of place, and why?


22.4A: History of Bacterial Diseases
- Give examples of historical, new, and re-emerging bacterial diseases in humans
There are records about infectious diseases as far back as 3000 B.C.E. A number of significant pandemics caused by bacteria have been documented over several hundred years. Some of the most memorable pandemics led to the decline of cities and nations. In the 21 st century, infectious diseases remain among the leading causes of death worldwide, despite advances made in medical research and treatments in recent decades. A disease spreads when the pathogen that causes it is passed from one person to another. For a pathogen to cause disease, it must be able to reproduce in the host’s body and damage the host in some way.
The Plague of Athens
In 430 B.C.E., the Plague of Athens killed one-quarter of the Athenian troops that were fighting in the great Peloponnesian War and weakened Athens’ dominance and power. The plague impacted people living in overcrowded Athens as well as troops aboard ships that had to return to Athens. The source of the plague may have been identified recently when researchers from the University of Athens were able to use DNA from teeth recovered from a mass grave. The scientists identified nucleotide sequences from a pathogenic bacterium, Salmonella enterica serovar typhi, which causes typhoid fever . This disease is commonly seen in overcrowded areas and has caused epidemics throughout recorded history.
Bubonic Plagues
From 541 to 750 C.E.., an outbreak of what was likely a bubonic plague (the Plague of Justinian), eliminated one-quarter to one-half of the human population in the eastern Mediterranean region. The population in Europe dropped by 50 percent during this outbreak. The bubonic plague would strike Europe more than once.
One of the most devastating pandemics was the Black Death (1346 to 1361) that is believed to have been another outbreak of bubonic plague caused by the bacterium Yersinia pestis . It is thought to have originated initially in China and spread along the Silk Road, a network of land and sea trade routes, to the Mediterranean region and Europe, carried by rat fleas living on black rats that were always present on ships. The Black Death reduced the world’s population from an estimated 450 million to about 350 to 375 million. Bubonic plague struck London hard again in the mid-1600s. In modern times, approximately 1,000 to 3,000 cases of plague arise globally each year. Although contracting bubonic plague before antibiotics meant almost certain death, the bacterium responds to several types of modern antibiotics; mortality rates from plague are now very low.
Migration of Diseases to New Populations
Over the centuries, Europeans tended to develop genetic immunity to endemic infectious diseases, but when European conquerors reached the western hemisphere, they brought with them disease-causing bacteria and viruses, which triggered epidemics that completely devastated populations of Native Americans who had no natural resistance to many European diseases. It has been estimated that up to 90 percent of Native Americans died from infectious diseases after the arrival of Europeans, making conquest of the New World a foregone conclusion.
Emerging and Re-emerging Diseases
The distribution of a particular disease is dynamic. Therefore, changes in the environment, the pathogen, or the host population can dramatically impact the spread of a disease. According to the World Health Organization (WHO), an emerging disease is one that has appeared in a population for the first time, or that may have existed previously, but is rapidly increasing in incidence or geographic range. This definition also includes re-emerging diseases that were previously under control. Approximately 75 percent of recently-emerging infectious diseases affecting humans are zoonotic diseases. Zoonoses, diseases that primarily infect animals and are transmitted to humans, are of both viral and bacterial origins. Brucellosis is an example of a prokaryotic zoonosis that is re-emerging in some regions. Necrotizing fasciitis (commonly known as flesh-eating bacteria) has been increasing in virulence for the last 80 years, for unknown reasons.
Some of the currently-emerging diseases are not actually new, but are diseases that were catastrophic in the past. They devastated populations, became dormant for a while, but have re-emerged, sometimes more virulent than before. Such was the case with bubonic plague. Other diseases, like tuberculosis, were never eradicated, but were under control in some regions of the world until re-emerging, mostly in urban centers with high concentrations of immunocompromised people. The WHO has identified certain diseases whose worldwide re-emergence should be monitored. Among these are two viral diseases (dengue fever and yellow fever) and three bacterial diseases (diphtheria, cholera, and bubonic plague). The war against infectious diseases has no foreseeable end.
Key Points
- A pathogen must be able to reproduce in the host’s body and damage the host in some way to cause disease.
- Before antibiotics, contracting plagues usually meant death; however, most bacterium associated with these plagues respond to modern antibiotics; mortality rates from these diseases are now very low.
- Emerging diseases include those that have appeared in a population for the first time or that may have existed previously, but are rapidly spreading; this also includes re-emerging diseases that were previously under control.
- The spread of disease can be impacted dramatically by changes in the environment, the pathogen, or the host population.
Key Terms
- zoonosis : an animal disease that can be transmitted to humans
- plague : an epidemic or pandemic caused by any pestilence
- pathogen : any organism or substance, especially a microorganism, capable of causing disease, such as bacteria, viruses, protozoa, or fungi


1.21.7: Thermodynamics and Kinetics
A given system at temperature \(\mathrm{T}\) and pressure \(\mathrm{p}\) is prepared using \(\mathrm{n}_{1}\) moles of water(\(\ell\)), the solvent, together with \(\mathrm{n}_{\mathrm{X}}^{0}\) and \(\mathrm{n}_{\mathrm{Y}}^{0}\) moles of chemical substances \(\mathrm{X}\) and \(\mathrm{Y}\) respectively at time ‘\(\mathrm{t} = 0\)’. The molalities of these solutes are \(\mathrm{m}_{\mathrm{X}}^{0}\left(=\mathrm{n}_{\mathrm{X}}^{0} / \mathrm{n}_{1} \, \mathrm{M}_{1}=\mathrm{n}_{\mathrm{X}}^{0} / \mathrm{w}_{1}\right)\) and \(\mathrm{m}_{\mathrm{Y}}^{0}\left(=\mathrm{n}_{\mathrm{Y}}^{0} / \mathrm{n}_{1} \, \mathrm{M}_{1}=\mathrm{n}_{\mathrm{Y}}^{0} / \mathrm{w}_{1}\right)\) respectively at time ‘\(\mathrm{t} = 0\)’; the concentrations are \(\mathrm{c}_{\mathrm{X}}^{0}\left(=\mathrm{n}_{\mathrm{XA}}^{0} / \mathrm{V}\right)\) and \(\mathrm{c}_{\mathrm{Y}}^{0}\left(=\mathrm{n}_{\mathrm{Y}}^{0} / \mathrm{V}\right)\) respectively.
Spontaneous chemical reaction leads to the formation of product \(\mathrm{Z}\). Here we consider this spontaneous change from the standpoints of chemical thermodynamics and chemical kinetics.
Thermodynamics
The spontaneous chemical reaction is driven by the affinity for chemical reaction, \(\mathrm{A}\) [1]. At each stage of the reaction the composition is described by the extent of reaction \(\xi\). The affinity \(\mathrm{A}\) is defined by the thermodynamic independent variables, \(\mathrm{T}, \mathrm{~p} \text { and } \xi\). Thus
\[\mathrm{A}=\mathrm{A}[\mathrm{T}, \mathrm{p}, \xi] \nonumber \]
Therefore
\[\mathrm{dA}=\left(\frac{\partial \mathrm{A}}{\partial \mathrm{T}}\right)_{\mathrm{p}, \xi} \, \mathrm{dT}+\left(\frac{\partial \mathrm{A}}{\partial \mathrm{p}}\right)_{\mathrm{T}, \xi} \, \mathrm{dp}+\left(\frac{\partial \mathrm{A}}{\partial \xi}\right)_{\mathrm{T}, \mathrm{p}} \, \mathrm{d} \xi \nonumber \]
At constant \(\mathrm{T}\) and \(\mathrm{p}\),
\[\mathrm{dA}=\left(\frac{\partial \mathrm{A}}{\partial \xi}\right)_{\mathrm{T}, \mathrm{p}} \, \mathrm{d} \xi \nonumber \]
In terms of thermodynamics, the reference point is thermodynamic equilibrium where the affinity for spontaneous change is zero and the composition is \(\xi^{\mathrm{eq}}\).
Chemical Kinetics
In the context of chemical reaction in solution, the system under study is, conventionally, a very dilute solution so that from a macroscopic standpoint the system at ‘\(\mathrm{t} = 0\)’ is slightly displaced from equilibrium where \(\mathrm{A}\) is zero. Thus chemists exploit their skill in monitoring for a solution the change with time of the absorbance at fixed wavelength, electrical conductivity, pH…. In a key assumption, the rate of change of composition \(\mathrm{d}\xi / \mathrm{~dt}\) is proportional to the affinity \(\mathrm{A}\) for spontaneous change[2];
\[\mathrm{d} \xi / \mathrm{dt}=\mathrm{L} \, \mathrm{A} \nonumber \]
Here \(\mathrm{L}\) is a phenomenological constant describing, in the present context, the phenomenon of spontaneous chemical reaction.
In general terms for processes at fixed temperature and pressure, the phenomenological property \(\mathrm{L}\) is related the isobaric – isothermal dependence of affinity \(\mathrm{A}\) on extent of chemical reaction by a relaxation time \(\tau_{\mathrm{T}, \mathrm{p}}\). Thus
\[\mathrm{L}^{-1}=-\left(\frac{\partial \mathrm{A}}{\partial \xi}\right)_{\mathrm{T}, \mathrm{p}} \, \tau_{\mathrm{T}, \mathrm{p}} \nonumber \]
Relaxation time \(\tau_{\mathrm{T},\mathrm{p}\) is a macroscopic property of a given system (at defined \(\mathrm{T}\) and \(\mathrm{p}\)) which chemists understand in terms of spontaneous chemical reaction (in a closed system). The task for chemists is to identify the actual chemical reaction in a given closed system.
Thermodynamics and Chemical Kinetics
In most treatments of chemical reactions the reference state is chemical equilibrium [3] where away from equilibrium the property \(\mathrm{dA}\) equals the affinity \(\mathrm{A}\) on the grounds that at equilibrium, \(\mathrm{A}\) is zero; \(\mathrm{A}=\mathrm{A}-\mathrm{A}^{\mathrm{eq}}=\mathrm{A}-0\). Hence combination of equations (c), (d) and (e) yields the key kinetic-thermodynamic equation.
\[\frac{\mathrm{d} \xi}{\mathrm{dt}}=-\mathrm{A} \,\left(\tau_{\mathrm{T}, \mathrm{p}}\right)^{-1} \,\left(\frac{\partial \mathrm{A}}{\partial \xi}\right)_{\mathrm{T}, \mathrm{p}}^{-1} \nonumber \]
Equation (6) relates the rate of change of composition to the affinity for chemical reaction and relaxation time \(\tau_{\mathrm{T}, \mathrm{p}}\). Equation (f) is therefore the key equation describing spontaneous chemical reaction in a closed system. In this context we stress the importance of equation (f).
Law of Mass Action
Equation (f) is an interesting and important description of the kinetics of chemical reaction. In fact the link between the rate of chemical reaction (\(\mathrm{d} \xi / \mathrm{dt}\)) and the affinity for spontaneous change \(\mathrm{A}\) is intuitively attractive. However while one may monitor the dependence of composition on time, \(\mathrm{d} \xi / \mathrm{dt}\), it is not immediately obvious how one might estimate the affinity \(\mathrm{A}\) and the property \(\left(\frac{\partial \mathrm{A}}{\partial \xi}\right)_{\mathrm{T}, \mathrm{p}}\) at time \(\mathrm{t}\). The Law of Mass Action offers a way forward although this law does not emerge from either the First or Second Laws of Thermodynamics. As Hammett [4] notes the Law of Mass Action was ‘first derived from limited observations’ and became ‘established through accumulation of observations with the principle and in the absence of contradictory evidence’. After the ‘Dark Ages’, came the renaissance and ‘Bartlett and Ingold and Peterson… accepting without question or comment the validity of the law of mass action’ [4].
The link back to thermodynamics was constructed using Transition State Theory developed by Eyring and described by Glasstone, Laidler and Eyring [5]. Therefore the phenomenological Law of Mass Action was brought into the fold of thermodynamics by offering a language which allowed activation parameters to be understood in terms of, for example, standard enthalpies and standard isobaric heat capacities of activation.
Footnotes
[1] I. Prigogine and R. Defay, Chemical Thermodynamics, (transl. D. H. Everett) Longmans Green, London, 1954.
[2] See for example, M. J. Blandamer, Introduction to Chemical Ultrasonics, Academic Press, London, 1973.
[3] E. F. Caldin, Fast Reactions in Solution, Blackwell, Oxford, 1964.
[4] L. P. Hammett, Physical Organic Chemistry, McGraw-Hill, New York, McGraw-Hill, New York, 2nd. edition, 1970, p.94.
[5] S. Glasstone, K. J. Laidler and H. Eyring, The Theory of Rate Processes, McGraw-Hill, New York,1941.


7: Leveraging Information Technology (IT) for Competitive Advantage
Learning Objectives
Upon successful completion of this chapter, you will be able to:
- Describe Porter’s competitive forces model and how information technology impacts competitive advantage.
- Describe Porter’s value chain model and its relationship to IT.
- Describe information systems that can provide businesses with a competitive advantage.
- Describe the collaborative systems that workers can use to contribute to their organization.
- Distinguish between a structured and an unstructured decision and its connection to IT.
- Discuss the challenges associated with a sustainable competitive advantage.
This chapter examines the impact that information systems have on organizations, how they can use IT to develop and sustain competitive advantages and improve operational effectiveness in their value chain and decision-making processes. We will discuss seminal works by Brynjolfsson, Carr, and Porter related to IT and competitive advantage.
-
- 7.3: Competitive Advantage
- What does it mean when a company has a competitive advantage? What are the factors that play into it? According to Michael Porter in his book “Competitive Advantage: Creating and Sustaining Superior Performance,” a company is said to have a competitive advantage over its rivals when it can sustain profits that exceed the industry's average.


7.1: Distribution and Density Functions
In the unit on Random Variables and Probability we introduce real random variables as mappings from the basic space \(\Omega\) to the real line. The mapping induces a transfer of the probability mass on the basic space to subsets of the real line in such a way that the probability that \(X\) takes a value in a set \(M\) is exactly the mass assigned to that set by the transfer. To perform probability calculations, we need to describe analytically the distribution on the line. For simple random variables this is easy. We have at each possible value of \(X\) a point mass equal to the probability \(X\) takes that value. For more general cases, we need a more useful description than that provided by the induced probability measure \(P_X\).
The Distribution Function
In the theoretical discussion on Random Variables and Probability , we note that the probability distribution induced by a random variable \(X\) is determined uniquely by a consistent assignment of mass to semi-infinite intervals of the form \((-\infty, t]\) for each real \(t\). This suggests that a natural description is provided by the following.
Definition
The distribution function \(F_X\) for random variable \(X\) is given by
\(F_X(t) P(X \le t) = P(X \in (-\infty, t])\) \(\forall t \in R\)
In terms of the mass distribution on the line, this is the probability mass at or to the left of the point t . As a consequence, \(F_X\) has the following properties:
- (F1) : \(F_X\) must be a nondecreasing function, for if \(t > s\) there must be at least as much probability mass at or to the left of \(t\) as there is for \(s\).
- (F2) : \(F_X\) is continuous from the right, with a jump in the amount \(p_0\) at \(t_0\) iff \(P(X = t_0) = p_0\). If the point \(t\) approaches \(t_0\) from the left, the interval does not include the probability mass at \(t_0\) until \(t\) reaches that value, at which point the amount at or to the left of t increases ("jumps") by amount \(p_0\); on the other hand, if \(t\) approaches \(t_0\) from the right, the interval includes the mass \(p_0\) all the way to and including \(t_0\), but drops immediately as \(t\) moves to the left of \(t_0\).
- (F3) : Except in very unusual cases involving random variables which may take “infinite” values, the probability mass included in \((-\infty, t]\) must increase to one as t moves to the right; as \(t\) moves to the left, the probability mass included must decrease to zero, so that \[F_X(-\infty) = \lim_{t \to - \infty} F_X(t) = 0\] and \[F_X(\infty) = \lim_{t \to \infty} F_X(t) = 1\]
A distribution function determines the probability mass in each semiinfinite interval \((\infty, t]\). According to the discussion referred to above, this determines uniquely the induced distribution.
The distribution function \(F_X\) for a simple random variable is easily visualized. The distribution consists of point mass \(p_i\) at each point \(t_i\) in the range. To the left of the smallest value in the range, \(F_X(t) = 0\); as t increases to the smallest value \(t_1\), \(F_X(t)\) remains constant at zero until it jumps by the amount \(p_1\) ... \(F_X(t)\) remains constant at \(p_1\) until \(t\) increases to \(t_2\), where it jumps by an amount p 2 to the value \(p_1 + p_2\). This continues until the value of \(F_X(t)\) reaches 1 at the largest value \(t_n\). The graph of \(F_X\) is thus a step function, continuous from the right, with a jump in the amount \(p_i\) at the corresponding point \(t_i\) in the range. A similar situation exists for a discrete-valued random variable which may take on an infinity of values (e.g., the geometric distribution or the Poisson distribution considered below). In this case, there is always some probability at points to the right of any \(t_i\), but this must become vanishingly small as \(t\) increases, since the total probability mass is one.
The procedure ddbn may be used to plot the distribution function for a simple random variable from a matrix X of values and a corresponding matrix PX of probabilities.
Example \(\PageIndex{1}\): Graph of FX for a simple random variable
>> c = [10 18 10 3]; % Distribution for X in Example 6.5.1 >> pm = minprob(0.1*[6 3 5]); >> canonic Enter row vector of coefficients c Enter row vector of minterm probabilities pm Use row matrices X and PX for calculations Call for XDBN to view the distribution >> ddbn % Circles show values at jumps Enter row matrix of VALUES X Enter row matrix of PROBABILITIES PX % Printing details See Figure 7.1
Description of some common discrete distributions
We make repeated use of a number of common distributions which are used in many practical situations. This collection includes several distributions which are studied in the chapter " Random Variables and Probabilities ".
Indicator function . \(X = I_E P(X = 1) = P(E) = pP(X = 0) = q = 1 - p\). The distribution function has a jump in the amount \(q\) at \(t = 0\) and an additional jump of \(p\) to the value 1 at \(t = 1\).
Simple random variable \(X = \sum_{t_i} I_{A_i}\) (canonical form)
The distribution function is a step function, continuous from the right, with jump of \(p_i\) at \(t = t_i\) (See Figure 7.1.1 for Example 7.1.1)
Binomial (\(n, p\)). This random variable appears as the number of successes in a sequence of \(n\) Bernoulli trials with probability \(p\) of success. In its simplest form
\(X = \sum_{i = 1}^{n} I_{E_i}\) with \(\{E_i: 1 \le i \le n\}\) independent
\(P(E_i) = p\) \(P(X = k) = C(n, k) p^k q^{n -k}\)
As pointed out in the study of Bernoulli sequences in the unit on Composite Trials, two m-functions ibinom and cbinom are available for computing the individual and cumulative binomial probabilities.
Geometric (\(p\)) There are two related distributions, both arising in the study of continuing Bernoulli sequences. The first counts the number of failures before the first success. This is sometimes called the “waiting time.” The event {\(X = k\)} consists of a sequence of \(k\) failures, then a success. Thus
The second designates the component trial on which the first success occurs. The event {\(Y = k\)} consists of \(k - 1\) failures, then a success on the \(k\)th component trial. We have
We say \(X\) has the geometric distribution with parameter (\(p\)), which we often designate by \(X~\) geometric (\(p\)). Now \(Y = X + 1\) or \(Y - 1 = X\). For this reason, it is customary to refer to the distribution for the number of the trial for the first success by saying \(Y - 1 ~\) geometric (\(p\)). The probability of \(k\) or more failures before the first success is \(P(X \ge k) = q^k\). Also
This suggests that a Bernoulli sequence essentially "starts over" on each trial. If it has failed \(n\) times, the probability of failing an additional \(k\) or more times before the next success is the same as the initial probability of failing \(k\) or more times before the first success.
Example \(\PageIndex{2}\) : The geometric distribution
A statistician is taking a random sample from a population in which two percent of the members own a BMW automobile. She takes a sample of size 100. What is the probability of finding no BMW owners in the sample?
Solution
The sampling process may be viewed as a sequence of Bernoulli trials with probability \(p = 0.02\) of success. The probability of 100 or more failures before the first success is \(0.98^{100} = 0.1326\) or about 1/7.5.
Negative binomial (\(m, p\)). \(X\) is the number of failures before the \(m\)th success. It is generally more convenient to work with \(Y = X + m\), the number of the trial on which the \(m\)th success occurs. An examination of the possible patterns and elementary combinatorics show that
There are m –1 successes in the first \(k - 1\) trials, then a success. Each combination has probability \(p^m q^{k - m}\). We have an m-function nbinom to calculate these probabilities.
 He scores if he throws a 1 or a 6. What is the probability he scores five times in ten or fewer throws?
>> p = sum(nbinom(5,1/3,5:10)) p = 0.2131
An alternate solution is possible with the use of the binomial distribution . The \(m\)th success comes not later than the k th trial iff the number of successes in \(k\) trials is greater than or equal to \(m\).
>> P = cbinom(10,1/3,5) P = 0.2131
Poisson (\(\mu\)). This distribution is assumed in a wide variety of applications. It appears as a counting variable for items arriving with exponential interarrival times (see the relationship to the gamma distribution below). For large \(n\) and small \(p\) (which may not be a value found in a table), the binomial distribution is approximately Poisson (\(np\)). Use of the generating function (see Transform Methods) shows the sum of independent Poisson random variables is Poisson. The Poisson distribution is integer valued, with
Although Poisson probabilities are usually easier to calculate with scientific calculators than binomial probabilities, the use of tables is often quite helpful. As in the case of the binomial distribution, we have two m-functions for calculating Poisson probabilities. These have advantages of speed and parameter range similar to those for ibinom and cbinom.
\(P(X = k)\) is calculated by
P = ipoisson(mu,k)
, where \(k\) is a row or column vector of integers and the result \(P\) is a row matrix of the probabilities.
\(P(X \ge k)\) is calculated by
P = cpoisson(mu,k)
, where \(k\) is a row or column vector of integers and the result \(P\) is a row matrix of the probabilities.
Example \(\PageIndex{4}\) : Poisson counting random variable
The number of messages arriving in a one minute period at a communications network junction is a random variable N ∼ Poisson (130). What is the probability the number of arrivals is greater than equal to 110, 120, 130, 140, 150, 160 ?
>> p = cpoisson(130,110:10:160) p = 0.9666 0.8209 0.5117 0.2011 0.0461 0.0060
The descriptions of these distributions, along with a number of other facts, are summarized in the table DATA ON SOME COMMON DISTRIBUTIONS in Appendix C .
The Density Function
If the probability mass in the induced distribution is spread smoothly along the real line, with no point mass concentrations, there is a probability density function \(f_X\) which satisfies
\(P(X \in M) = P_X(M) = \int_M f_X(t)\ dt\) (are under the graph of \(f_X\) over \(M\))
At each \(t\), \(f_X(t)\) is the mass per unit length in the probability distribution. The density function has three characteristic properties:
(f1) \(f_X \ge 0\) (f2) \(\int_R f_X = 1\) (f3) \(F_X (t) = \int_{-\infty}^{t} f_X\)
A random variable (or distribution) which has a density is called absolutely continuous . This term comes from measure theory. We often simply abbreviate as continuous distribution.
- There is a technical mathematical description of the condition “spread smoothly with no point mass concentrations.” And strictly speaking the integrals are Lebesgue integrals rather than the ordinary Riemann kind. But for practical cases, the two agree, so that we are free to use ordinary integration techniques.
-
By the fundamental theorem of calculus
\(f_X(t) = F_X^{'} (t)\) at every point of continuity of \(f_X\)
- Any integrable, nonnegative function \(f\) with \(\int f = 1\) determines a distribution function \(F\), which in turn determines a probability distribution. If \(\int f \ne 1\), multiplication by the appropriate positive constant gives a suitable \(f\). An argument based on the Quantile Function shows the existence of a random variable with that distribution.
-
In the literature on probability, it is customary to omit the indication of the region of integration when integrating over the whole line. Thus
\(\int g(t) f_X (t) dt = \int_R g(t) f_X(t) dt\)
The first expression is not an indefinite integral. In many situations, \(f_X\) will be zero outside an interval. Thus, the integrand effectively determines the region of integration.
Some common absolutely continuous distributions
Uniform
\((a, b)\).
Mass is spread uniformly on the interval \([a, b]\). It is immaterial whether or not the end points are included, since probability associated with each individual point is zero. The probability of any subinterval is proportional to the length of the subinterval. The probability of being in any two subintervals of the same length is the same. This distribution is used to model situations in which it is known that \(X\) takes on values in \([a, b]\) but is equally likely to be in any subinterval of a given length. The density must be constant over the interval (zero outside), and the distribution function increases linearly with \(t\) in the interval. Thus,
The graph of \(F_X\) rises linearly, with slope 1/(\(b - a\)) from zero at \(t = a\) to one at \(t = b\).
Symmetric triangular
\((-a, a)\), \(f_X(t) = \begin{cases} (a + t)/a^2 & -a \le t < 0 \\ (a - t)/a^2 & 0 \le t \le a \end{cases}\).
This distribution is used frequently in instructional numerical examples because probabilities can be obtained geometrically. It can be shifted, with a shift of the graph, to different sets of values. It appears naturally (in shifted form) as the distribution for the sum or difference of two independent random variables uniformly distributed on intervals of the same length. This fact is established with the use of the moment generating function (see Transform Methods). More generally, the density may have a triangular graph which is not symmetric.
Example \(\PageIndex{5}\) : Use of a triangular distribution
Suppose \(X~\) symmetric triangular (100, 300). Determine \(P(120 < X \le 250)\).
Remark . Note that in the continuous case, it is immaterial whether the end point of the intervals are included or not.
Solution
To get the area under the triangle between 120 and 250, we take one minus the area of the right triangles between 100 and 120 and between 250 and 300. Using the fact that areas of similar triangles are proportional to the square of any side, we have
\(P = 1 - \dfrac{1}{2} ((20/100)^2 + (50/100)^2) = 0.855\)
Exponential
(\(\lambda\)) \(f_X(t) = \lambda e^{-\lambda t}\) \(t \ge 0\) (zero elsewhere).
Integration shows \(F_X(t) = 1 - e^{-\lambda t}\) (t \ge 0\) (zero elsewhere). We note that \(P(X > 0) = 1 - F_X(t) = e^{-\lambda t}\) \(t \ge 0\). This leads to an extremely important property of the exponential distribution. Since \(X > t + h\), \(h > 0\) implies \(X > t\), we have
Because of this property, the exponential distribution is often used in reliability problems. Suppose \(X\) represents the time to failure (i.e., the life duration) of a device put into service at \(t = 0\). If the distribution is exponential, this property says that if the device survives to time \(t\) (i.e., \(X > t\)) then the (conditional) probability it will survive \(h\) more units of time is the same as the original probability of surviving for \(h\) units of time. Many devices have the property that they do not wear out. Failure is due to some stress of external origin. Many solid state electronic devices behave essentially in this way, once initial “burn in” tests have removed defective units. Use of Cauchy's equation (Appendix B) shows that the exponential distribution is the only continuous distribution with this property.
Gamma distribution
\((\alpha, \lambda)\) \(f_X(t) = \dfrac{\lambda^{\alpha} t^{\alpha - 1} e^{-\lambda t}}{\Gamma (\alpha)}\) \(t \ge 0\) (zero elsewhere)
We have an m-function
gammadbn
to determine values of the distribution function for \(X~\) gamma \((\alpha, \lambda)\). Use of moment generating functions shows that for \(\alpha = n\), a random variable \(X~\) gamma \((n, \lambda)\) has the same distribution as the sum of \(n\) independent random variables, each exponential (\(lambda\)). A relation to the Poisson distribution is described in Sec 7.5.
Example \(\PageIndex{6}\) : An arrival problem
On a Saturday night, the times (in hours) between arrivals in a hospital emergency unit may be represented by a random quantity which is exponential (\(\lambda = 3\)). As we show in the chapter Mathematical Expectation , this means that the average interarrival time is 1/3 hour or 20 minutes. What is the probability of ten or more arrivals in four hours? In six hours?
Solution
The time for ten arrivals is the sum of ten interarrival times. If we suppose these are independent, as is usually the case, then the time for ten arrivals is gamma (10, 3).
>> p = gammadbn(10,3,[4 6]) p = 0.7576 0.9846
Normal, or Gaussian
\((\mu, \sigma^2)\) \(f_X (t) = \dfrac{1}{\sigma \sqrt{2 \pi}}\) exp \((-\dfrac{1}{2} (\dfrac{t - \mu}{\sigma})^2)\) \(\forall t\)
We generally indicate that a random variable \(X\) has the normal or gaussian distribution by writing \(X ~ N(\mu, \sigma^2)\), putting in the actual values for the parameters. The gaussian distribution plays a central role in many aspects of applied probability theory, particularly in the area of statistics. Much of its importance comes from the
central limit theorem
(CLT), which is a term applied to a number of theorems in analysis. Essentially, the CLT shows that the distribution for the sum of a sufficiently large number of independent random variables has approximately the gaussian distribution. Thus, the gaussian distribution appears naturally in such topics as theory of errors or theory of noise, where the quantity observed is an additive combination of a large number of essentially independent quantities. Examination of the expression shows that the graph for \(f_X(t)\) is symmetric about its maximum at \(t = \mu\).. The greater the parameter \(\sigma^2\), the smaller the maximum value and the more slowly the curve decreases with distance from \(\mu\).. Thus parameter \(\mu\). locates the center of the mass distribution and \(\sigma^2\) is a measure of the spread of mass about \(\mu\). The parameter \(\mu\) is called the
mean value
and \(\sigma^2\) is the
variance
. The parameter \(\sigma\), the positive square root of the variance, is called the
standard deviation
. While we have an explicit formula for the density function, it is known that the distribution function, as the integral of the density function, cannot be expressed in terms of elementary functions. The usual procedure is to use tables obtained by numerical integration.
Since there are two parameters, this raises the question whether a separate table is needed for each pair of parameters. It is a remarkable fact that this is not the case. We need only have a table of the distribution function for \(X ~ N(0,1)\). This is refered to as the
standardized normal
distribution. We use \(\varphi\) and \(\phi\) for the standardized normal density and distribution functions, respectively.
Standardized normal \(varphi(t) = \dfrac{1}{\sqrt{2 \pi}} e^{-t^2/2}\) so that the distribution function is \(\phi (t) = \int_{-\infty}^{t} \varphi (u) du\).
The graph of the density function is the well known bell shaped curve, symmetrical about the origin (see Figure 7.1.4). The symmetry about the origin contributes to its usefulness.
Note that the area to the left of \(t = -1.5\) is the same as the area to the right of \(t = 1.5\), so that \(\phi (-2) = 1 - \phi(2)\). The same is true for any \(t\), so that we have
This indicates that we need only a table of values of \(\phi(t)\) for \(t > 0\) to be able to determine \(\phi (t)\) for any \(t\). We may use the symmetry for any case. Note that \(\phi(0) = 1/2\),
Example \(\PageIndex{7}\) : Standardized normal calculations
Suppose \(X ~ N(0, 1)\). Determine \(P(-1 \le X \le 2)\) and \(P(|X| > 1)\)
Solution
- \(P(-1 \le X \le 2) = \phi (2) - \phi (-1) = \phi (2) - [1 - \phi(1)] = \phi (2) + \phi (1) - 1\)
- \(P(|X| > 1) = P(X > 1) + P(X < -1) = 1 - \phi(1) + \phi (-1) = 2[1 -\phi(1)]\)
From a table of standardized normal distribution function (see Appendix D ), we find
\(\phi(2) = 0.9772\) and \(\phi(1) = 0.8413\) which gives \(P(-1 \le X \le 2) = 0.8185\) and \(P(|X| > 1) = 0.3174\)
General gaussian distribution
For \(X~N(\mu, \sigma^2)\), the density maintains the bell shape, but is shifted with different spread and height. Figure 7.1.5 shows the distribution function and density function for \(X ~N(2, 0.1)\). The density is centered about \(t = 2\). It has height 1.2616 as compared with 0.3989 for the standardized normal density. Inspection shows that the graph is narrower than that for the standardized normal. The distribution function reaches 0.5 at the mean value 2.
A change of variables in the integral shows that the table for standardized normal distribution function can be used for any case.
Make the change of variable and corresponding formal changes
to get
\(F_X(t) = \int_{-\infty}^{(t-\mu)/\sigma} \varphi (u) du = \phi (\dfrac{t - \mu}{\sigma})\)
Example \(\PageIndex{8}\) : General gaussian calculation
Suppose \(X ~ N\)(3,16) (i.e., \(\mu = 3\) and \(\sigma^2 = 16\)). Determine \(P(-1 \le X \le 11)\) and \(P(|X - 3| > 4)\).
Solution
- \(F_X(11) - F_X(-1) = \phi(\dfrac{11 - 3}{4}) - \phi(\dfrac{-1 - 3}{4}) = \phi(2) - \phi(-1) = 0.8185\)
- \(P(X - 3 < -4) + P(X - 3 >4) = F_X(-1) + [1 - F_X(7)] = \phi(-1) + 1 - \phi(1) = 0.3174\)
In each case the problem reduces to that in Example.
We have m-functions
gaussian
and
gaussdensity
to calculate values of the distribution and density function for any reasonable value of the parameters.
The following are solutions of example 7.1.7 and example 7.1.8, using the m-function gaussian.
Example \(\PageIndex{9}\): Example 7.1.7 and Example 7.1.8 (continued)
>> P1 = gaussian(0,1,2) - gaussian(0,1,-1) P1 = 0.8186 >> P2 = 2*(1 - gaussian(0,1,1)) P2 = 0.3173 >> P1 = gaussian(3,16,11) - gaussian(3,16,-1) P2 = 0.8186 >> P2 = gaussian(3,16,-1)) + 1 - (gaussian(3,16,7) P2 = 0.3173
The differences in these results and those above (which used tables) are due to the roundoff to four places in the tables.
Beta \((r, s)\), \(r > 0\), \(s > 0\). \(f_X(t) = \dfrac{\Gamma(r + s)}{\Gamma(r) \Gamma(s)} t^{r - 1} (1 - t)^{s - 1}\) \(0 < t < 1\)
Analysis is based on the integrals
Figure 7.6 and Figure 7.7 show graphs of the densities for various values of \(r, s\). The usefulness comes in approximating densities on the unit interval. By using scaling and shifting, these can be extended to other intervals. The special case \(r = s = 1\) gives the uniform distribution on the unit interval. The Beta distribution is quite useful in developing the Bayesian statistics for the problem of sampling to determine a population proportion. If \(r, s\) are integers, the density function is a polynomial. For the general case we have two m-functions, beta and betadbn to perform the calculatons.
Weibull
\((\alpha, \lambda, v)\) \(F_X (t) = 1 - e^{-\lambda (t - v)^{\alpha}}\) \(\alpha > 0\), \(\lambda > 0\), \(v \ge 0\), \(t \ge v\)
The parameter \(v\)
is a shift parameter. Usually we assume \(v = 0\). Examination shows that for
α
=1 the distribution is exponential (\(\lambda\)). The parameter
α
provides a distortion of the time scale for the exponential distribution. Figure 7.6 and Figure 7.7 show graphs of the Weibull density for some representative values of \(\alpha\) and \(\lambda\) (\(v = 0\)). The distribution is used in reliability theory. We do not make much use of it. However, we have m-functions
weibull
(density) and
weibulld
(distribution function) for shift parameter \(v = 0\) only. The shift can be obtained by subtracting a constant from the \(t\) values.


8.9: El superlativo
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Objetivos
- Use superlative expressions
The superlative is used to make a comparison between multiple items and it is used to stress a relationship of superiority between one item and the rest. In English, to form a superlative we usually add “-est” to an adjective. In Spanish, however, we’re going to start with an article and add “más” / “menos” before adjective to create the superlative.
el/la/los/las + ( noun ) + más/menos + ( adjective ) + de …
Some adjectives have irregular comparative forms which you saw when discussing comparisons of inequality. When applied to the superlative constructions they retain their irregular forms:
definite article + irregular comparative form + de …
bueno →
el mejor
(
the best
)
malo →
el peor
(
the worst
)
grande →
el mayor
(
the oldest
–
people
)
pequeño →
el menor
(
the youngest
–
people
)
- Cuando los colegas coreanos salen a comer, el mayor paga. ( When Korean colleagues go out to eat, the oldest pays .)
- Muchos europeos son trilingües, pero en general los africanos son los más multilingües del mundo. ( Many Europeans are trilingual, but in general Africans are the most multilingual in the world .)
Attributions
- Gramu00e1tica: El superlativo. Authored by : SUNY Oneonta with Lumen Learning. License : CC BY: Attribution
- Los yoghurts mas frescos. Authored by : Brigeth Rivera . License : CC BY: Attribution


No single observation can give you all the information you will need about a child’s development. In order to truly understand a child’s unique attributes, preferences, personality and strengths, you must observe them consistently, using several documentation tools and techniques. Each observation method has strengths and limitations. In this section, we will review some of the more commonly used techniques and tools that teachers use to gather objective observation evidence: Running Record; Checklists; Frequency Count; Anecdotal Record; Work Sample; Learning Story; and Technology.
Running Record
One of the oldest observation methods used in early child education is the Running Record. Running Records are considered by some as an “informal method” of observation as compared to
Narrative Description
or
Specimen Records
which are considered to be a more “formal method” of collecting data. The primary difference between the two methods is that with a Running Record, evidence is gathered in a more spontaneous (informal) manner as it occurs, whereas with a Narrative Description a (formal) plan would be arranged in advance, prior to the observation. More specifically, you would schedule a day, time and setting, you would select a specific child or group of children, and you would decide on the purpose, reason or focus of your observation (e.g. cognitive skills, social interactions, play patterns). Both methods provide rich, detailed evidence and both methods provide written accounts of everything you see and hear a child doing during a specific timeframe (Bentzen, 2009).
For the purpose of this text, we will use the term Running Record and recommend that you, as an intentional teacher, conduct Running Records (whether spontaneous or planned, informal or formal) as part of your regular or routine observations. The primary goal for using a Running Record is to “obtain a detailed, objective account of behavior without inference, interpretations, or evaluations” (Bentzen, 2009, p.112). You will know you have gathered good evidence when you can close your eyes and you can “see” the images in your mind as they are described in your Running Record (Bentzen, 2009).
Collecting Your Data
All you need is time, paper and a pen to gather your observation evidence. The goal with a running record is to write down everything you see and hear - exactly as it occurs, without adding any comments or attaching any opinions. As the saying goes, “just the facts, ma’am!” With the Running Record format, not only will you highlight children’s behaviors, you will record the “setting, situation and sequence” in which the behavior occurred. Be as descriptive as possible and yet be as concise as possible. Children move quickly, so you must write quickly. When conducting a running record, you need to be out of ratio. You are to step back and observe from a distance. Do not interfere with the child’s natural play, do not ask questions and do not run after them. Be as invisible as possible.
Organizing your Data
As you collect rich, detailed data throughout the school year, you will begin to recognize patterns of development, and you will see each child’s unique attributes, personalities, and abilities as they emerge. Be sure to date all your running records; having 12-24 children in your classroom can add up to a lot of running records. You will need to store your running records safely in a portfolio or file folder. When it comes time to assess a child’s development, you will be able to look back and review all the evidence you have collected and to monitor the child’s progress over time.
Note: A Running Record is an ideal observation method for “students”. Teachers may not always have the time or staff coverage to conduct a Running Record.
Table \(\PageIndex{1}\): Running Record
Advantages
Disadvantages
Provides detailed data about the who, what, where, and when
Evidence is documented as it occurs, in a sequence
Provides objective and descriptive evidence
Appropriate for gathering baseline information about the child’s interests, abilities and skill level
Ideal for tracking a child’s development over time
Less structured, more free flowing
Evidence can be gathered formally or informally
Interpretations and reflections can be added later
Time consuming
May be difficult to keep up and follow along as children move quickly from one activity to another
Not a practical technique for teachers who are in ratio
Behaviors may not be typical for that observation day as compared to other days
Let’s Practice Gathering Evidence
Example 1:
Running Record: On 7/2/2019, Jorge played in the sandbox for 20 minutes.
What did you “see” with this example? What was the setting, situation and sequence of events?
What did you learn about Jorge?
Was the evidence objective? Was the evidence descriptive?
Let’s try again.
Example 2:
Running Record: 7/2/2019. Time: 10:10am
During outside play and exploration, the following activities were available: bikes, sandbox, sensory table with goop, hula hoops, balls and a reading area with a basket of books. Jorge played in the sandbox for 20 minutes.  Jorge asked Julissa if he could have the dinosaur, “When you are finished, can I have the dinosaur for my cave?” Julissa handed Jorge the dinosaur and said, “Can I see?” Jorge nodded his head up and down.
At 10:30am, the teacher announced that it was time to clean up. Jorge stood up, dropped his shovel, ran over to the door and got in line. While in line, Jorge waved his hands and said “Come on Max. Come on. Here. Come here.” Max ran over and stood next to Jorge in line.
What did you “see” with this example? What was the setting, situation, and sequence of events?
What did you learn about Jorge?
Was the evidence objective? Was the evidence descriptive?
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Running Record Template #1
Date:
Start Time:
End Time:
Setting:
Activity Area:
Who did you observe:
Running Record
Running Record Template #2
Date:
Start Time:
End Time:
Setting:
Activity Area:
Who did you observe:
Running Record
Interpretation
Frequency Counts (Time or Event Sampling)
A Frequency Count is an informal observation method that is used to gather information about a child’s interests, social interactions, play patterns, and temperamental traits. As the teacher observes the children at play, a tally mark is made every time the noted behavior or action occurs within a set timeframe. Frequency Counts are also used to track
undesirable or challenging behaviors, as well as ideal or positive behaviors.
Collecting your data
To create a Frequency Count, you must first decide on what social interactions, behaviors, interest areas, or types of play you want to monitor. You may decide to track your child during one focused activity or timeframe, or you may map out what a typical day might look like for your child and track all the interactions and experiences they engage in throughout the day. Either way, as you observe your child, you will make a tally mark every time they play in a specified area or display one of the action items as listed on your Frequency Count.
Here are some examples of how you might use a Frequency Count to gather data:
Sue has been hitting a lot lately and displaying other challenging behaviors
. You will want to track how many times she hits in a typical day, along with any other challenging behaviors. You will also want to track
where
the incidents are occurring – are there more incidents while inside the classroom or are things happening during outside play? You will want to look at
when
the incidents are occurring most often– are there more incidents earlier in the day or later in the day? You may want to observe what is happening at drop-off time, mealtime and at naptime. Lastly, you may want to track
who
Sue is socializing with and
how
she plays with others. Does Sue display a consistent play pattern (parallel play, cooperative play, onlooker play)?
Thomas is a new student and his mother wants to know how he is doing.
You may want to observe which centers Thomas goes to most often throughout the day and track his interests. You may also want to track whether he plays alone or with other children.
You and a child in your class are constantly butting heads
. How can you create a supportive environment and provide a “goodness of fit?” You may need to track the child’s temperamental traits and observe how the child approaches activities and how they respond to social situations.
Organizing Your Data
After you have collected all the data for that timeframe, count the tally marks. What can you interpret from this data? What areas or action items received a high number of tally marks? What areas or action items received a low number of tally marks? Do you see any patterns? As you consider those questions, reflect on a plan of action that you might use to further support that child’s development.
Table \(\PageIndex{2}\): Advantages and Disadvantages of Frequency Data
Advantages
Disadvantages
Quick and easy to use, and no training is required
Can be personalized or designed to gather specific baseline data (play patterns, challenging behaviors, social situations, temperamental traits)
Provides immediate quantifiable data
Ideal for tracking behaviors over time and for noting an increase or decrease of incidents
Can be useful when planning behavior modification strategies
Data can be graphed or charted to find consistent patterns
Does not provide rich details or context like anecdotal notes or running records
There is no clear sequence of events regarding certain actions or behaviors
(Although the behavior is tracked, information about the antecedent and the consequence is missing)
Does not provide qualitative evidence
Results may be misleading
Checklists
Checklists are an efficient and practical way to collect information about a child’s development. Checklists are based on “developmental norms” as determined by developmental theorists. With each age range, there are certain expectations and skills that a child should be able to achieve. Checklists are designed to track a child’s competencies in all the developmental domains including physical, cognitive, language, social and emotional. With a checklist, teachers can easily see what a child
can do,
as well as note what areas of development need further support. Teachers can create their own checklists based on certain skill sets, or they can download a formal developmental milestone checklist from a reputable source to look at a child’s full range of development. Checklists can be used to track a large group of children or an individual child.
Collecting your data
Whether you design your own checklist or download one, use it regularly to collect data. The checklist can be utilized in two ways:
You can observe a child on a specific day while they are engaged in an activity (either child-directed or teacher-directed). As you observe, you will check off the skills or milestones that the child
can do
on that day, at that moment.
You can also review data from other observations (e.g. running records or anecdotal notes, work samples) that you collected, and ADD any other skills or milestones that were mastered during those previous observations.
*Note: It is vital that you note the dates that you observed the skills being mastered. A check mark alone will limit the reliability and validity
Organizing your data
Schedule a day and time to regularly review your observation data. Data collected from other observations (mastered milestones and developing skill sets) can be added to the checklist so you can clearly see a child’s progress over time. You may use colored pens to track all the different dates that milestones were achieved. As you review the checklist, what can you interpret from this data? Does the child demonstrate strengths in any of the developmental domains or areas of learning? Which milestones and skills need further support? As you consider those questions, reflect on a plan of action that you might use to further support that child’s development. How can you provide opportunities for the child to gain more practice? What adjustments need to be made to make the activity more challenging? What extensions can be added to continue the learning pattern?
[24]
Table \(\PageIndex{3}\): Advantages and Disadvantages of Checklists
Advantages
Disadvantages
Ideal for tracking a child's progress over time
Different observers (the teacher, assistant or a support team) can check off skills that they observe the child doing
Checklists can be created to measure specific areas of development, or a subset of developmental skills
Checklists can be used to observe a group of children or an individual child
Checklists are quick and easy to use, and no training is required
Checklists can be used in conjunction with other observations
Checklists highlight the developmental strengths a child has mastered, as well as those skills that need further support
Developmental Milestone Checklists are readily available on-line through various agencies (i.e. Center for Disease Control)
Data can help plan curriculum activities
Checklists do not provide rich details or context like anecdotal notes or running records
There is no clear sequence of events to regarding certain actions or behaviors
Checklists focus on developmental norms and typical development with no regard for environment, family influences, cultural influences and individual development
Teachers tend to focus on the skills and milestones that haven’t been mastered, focusing on the deficits rather than highlighting the strengths. This can make the child and parents feel as if they have failed or add unnecessary stress
Checklists must be updated regularly using other observation methods
Checklist for Physical Milestone
Perceptual Movement
Skills
Can Do
Needs Further Support
Date and Evidence
Moves in a zig-zag pattern – able to change directions with ease
Plays follow the leaders and mirrors others movements
Moves body to music cues
Speeds up and slows down while running or riding bike
Gross Motor Movement
Skills
Can Do
Needs Further Support
Date and Evidence
Completes tasks on an obstacle course
Changes directions and stops quickly while running
Pumps legs on a swing
Runs and uses arm and legs in opposition
Climbs
Walks up and down stairs with one foot on each stair step
Hops on one foot
Kicks balls
Catches and throws (bean bags and balls)
Pedals a 3-wheeled bike (tricycle)
Bounces a ball several times
Walks along a balance beam
Jumps up and down, jumps forward using arms
Fine Motor Movement
Skills
Can Do
Needs Further Support
Date and Evidence
Cuts with scissors
Uses writing utensils (markers, crayons, pencils) to scribble
Prints letters, numbers
Uses stamps and stamp pad
Strings beads
Pours liquid into cup
Manipulates, moves and picks up small objects
Uses utensils to feed self
Buttons and zips
Peels a banana or orange
Opens and closes a Ziploc baggie
Scoops and pours materials (sand, dirt, rocks, beads)
Anecdotal Records
An Anecdotal Record is “an informal observation method often used by teachers as an aid to understanding the child’s personality or behavior. It provides a running account of behavior that is either typical or unusual for the child” (Bentzen, 2009, p. 178). Anecdotal Records, also referred to as “anecdotal notes,” are direct observations of a child that offer a window of opportunity to see into a child’s actions, interactions and reactions to people and events. An Anecdotal Record is an excellent tool that provides teachers with a collection of narratives that can be used to showcase a child’s progress over time. As compared to a Running Record, Anecdotal Records provide brief notes that are focused on a specific event or activity.
Collecting Your Data
To gather effective observation evidence, you need to include the following components:
Accurate and specific details of the event (vivid descriptions exactly as you see and hear them happening - do not summarize, assume or make judgments)
The context, setting and situation that surrounds the event (the where, when, who, what, and how)
Objective facts about the child’s behavior and interactions (report actions and conversations)
Write records in the past tense
Here are some examples of observation evidence you might want to gather:
Social interactions with peers
Everyday routines, like mealtime and transition times
How they utilize materials at the various centers (library, block, math, science, art, music)
How they engage in teacher-directed activities (structured learning opportunities)
How they engage in child-directed activities (open exploration opportunities)
How they are inside and how they are outside
Organizing your Data
Once you have completed the Anecdotal Record you will take a moment to interpret the data. You will look for
patterns
and you will note whether the data reflects
typical or unusual behavior
for the child. To measure a child’s developmental progress, you will look for their
strengths
(skills and milestones that have been mastered) and their
needs
(skills and
milestones that the child needs further support with). The summary notes help you to clarify
instructional recommendations (adjustments that you will make to the environment to accommodate the child’s individual learning style). The notes you take can help you generate developmentally appropriate lesson plan activities and interactions. All Anecdotal Records need to be dated and stored safely in the child’s portfolio or file folder.
Table \(\PageIndex{4}\): Advantages and Disadvantages of Anecdotal Record
Advantages
Disadvantages
Provides vivid details about the who, what, when, where and how
Takes less time to write up an observation as compared to using Running Records
Evidence is documented as it occurs, in a sequence
Provides objective and descriptive evidence
Interpretation notes can be added afterwards
Evidence can be gathered formally (planned) or informally (spontaneously)
No special training is required
Provides qualitative data over time and is helpful in tracking changes in a child’s development over time
Data can be tainted if it is not written in the moment
Focuses on one event, situation or behavior at a time and can miss or overlook important information
Does not provide quantitative data results
4. May not always report a child’s typical pattern of development or behavior
Teachers have been collecting pieces of children’s artwork and posting them on the classroom walls forever. Not only do the children enjoy seeing their work of art on display, parent’s appreciate seeing their child’s work as well! To create an official work sample however takes more effort than hanging a picture on the wall. What exactly is a work sample? A work sample is a tangible piece of evidence that showcases a child’s effort, progress and achievement. More specifically, not only does a work sample highlight the final
product
, it can highlight the
process
as well, by highlighting the child’s problem-solving efforts, experimentation methods or collaboration skills. Work samples are
authentic artifacts
that provide information about the child’s learning experience.
Collecting your data
Work samples can be gathered throughout the school year. Typically, you would collect a variety of samples that highlight the child’s overall development in each of the developmental areas: Physical; Cognitive; Language; Social -Emotional. More specifically, you might include a child’s drawing or painting, a writing sample from their journal, a cutting sample, or photographs of the child engaged in activities such as building a block tower or sandcastle or riding a bike.
Organizing your data
Whether you post a work sample on the classroom wall (using a
documentation board
) or you collect a sample for a child’s portfolio, you must add documentation. Not only will documentation help families recognize the value of play, it reinforces the concept that every activity is an opportunity to learn. For accuracy, be sure to include the following information: Child’s Name; Date; Setting; and an Anecdotal Note with a description about how and why the sample was collected. Work samples should be organized in a chronological manner to showcase progress over time. Be sure to store work samples in a safe place like a file-folder or portfolio, or electronically in a computer file.
Table \(\PageIndex{5}\): Advantages and Disadvantages of Work Samples
Advantages
Disadvantages
Provides tangible/ visible evidence that teachers can use to track a child’s learning, growth and development over time
Parents and children both enjoy seeing the work on display
Provides authentic documentation which is ideal for assessment
Teachers can use information to plan and adjust curriculum to help children achieve their learning goals
Families can see how children learn through play
Children can share their insights as to
how
they created the work sample and offer their perspectives as to
what
they were thinking (authentic evidence)
Children enjoy seeing their work on display and they can feel empowered when their work is valued
Can be time consuming adding anecdotal documentation and creating documentation boards
Requires ample storage space
Requires a financial investment in technology (camera, video or audio recorder)
Concerns over confidentiality and privacy when using photos, audio or videos
Work Sample Template
Learning Stories
In an article published in NAEYC’s Teaching Young Children, Judy Pack shares her thoughts on Learning Stories, “I like to think of it as observing small moments that provide big opportunities.”
[26]
As compared to Running Records or Anecdotal Notes, a Learning Story is an observation method that is written in a
narrative story format
to highlight a child’s learning. The Learning Story communicates more than facts about how a child approaches or accomplishes tasks, it spotlights key moments in a child’s day and focuses on their strengths. When writing a Learning Story, a teacher not only writes down what she saw and heard, she can also write down what she thought about while she watched the child play. More than that, this method encourages the child and their families to be active participants in the reflective process. When the teacher shares the Learning Story with both the child and family members, they can add their comments, ask follow-up questions and make suggestions on how to move forward based on what was reported in the Learning Story. One unique aspect of Learning Stories is that when used regularly, they can help teachers connect to families and build strong, respectful relationships.
[27]
Gathering your data
Whether you plan an observation, or you spontaneously watch a child as they play, and whether you observe during a teacher-directed activity or during a child-directed moment, you can gather some suitable evidence for your Learning Story. As you watch and listen to a child at play, you can take some pictures and jot down some objective and descriptive facts that you will use to write a story. As suggested by Park (2016), if you want to learn about a child’s interests and capabilities, and how they process information; you will want to watch the following:
Engagement: How long does the child stay focused and engaged in an activity?
Intentionality: Does the child have a goal in mind or express a plan of action?
Relationships: Does the child interact or connect with others?
Learning disposition: Does the child have a particular approach to figuring things out or a preferred style of learning?
[28]
Organizing your data
Whether you want to write a short paragraph or a full page, there are some key components that you must include in your Learning Story. We will refer to the EarlyWorks tool and the guidelines as recommended by Tom Drummond to write up your observation data.
[29]
Your Learning Story should include the following:
A Title
– All good stories have a title that draws the reader in. Titles can act as a reminder of the content of the learning story, making it easy for educators to revisit at a later time.
Photos
– Learning Stories should have at least one photo. Visual images evoke emotion and a connection to the story.
Narrative
– This is where the storyteller (you) describes what is seen and heard. It is best to write in the first person, using “I…”. The narrative is the body of the story and highlights authentic observation evidence (facts and vivid details).
What it means
– This is where the storyteller (you)
interprets
the learning that took place. It is best to write in the second person, using “You…”.
Opportunities and Possibilities
– This is where you reflect on planning for the next step and building on what the child knows.
Family & Child’s Voice
– The child’s family is encouraged to provide their understanding of the story. Families can create stories and provide valuable insight into the learning that happens at home. Children can also share their perspectives.
[30]
*Note: A Learning Story Template is available
Table \(\PageIndex{6}\): Advantages and Disadvantages of Learning Stories
Advantages
Disadvantages
The child receives positive messages that their ideas and way of thinking are valued and they enjoy hearing stories about their successes
The teacher, child and family have an equal opportunity to reflect on the child’s thinking and learning
The stories provide insight into the best way to plan for a more meaningful curriculum.
The stories capture moments in a child’s daily life that can be used with other observation tools to create a comprehensive profile on a child
Provides authentic information about a child’s strengths in a friendly and personal format
Informs families how children learn through play and how they are natural learners, eager investigators, and problem solvers.
Opens a door for respectful conversations with parents about school experiences
Can be time consuming
Can be difficult to remain objective
Focuses on one event, situation or behavior at a time and can miss or overlook important information
Does not provide quantitative data
results
May not always report a child’s typical pattern of development or behavior
Learning Story Template
Technology
Finding ways to utilize technology into regular routines can make collecting observation evidence much more efficient for busy teachers. Photographs, video, and audio recordings can authentically capture children’s explorations, investigations, play and learning experiences in the actual moment. With this type of documentation, teachers can replay key moments in a child’s day to look for specific interactions, play patterns, developmental milestones, struggles and accomplishments. With this technique, teachers can also listen for language development by recording actual conversations that children are having with their peers. Teachers can also monitor how children problem solve and can tape special moments as well as capture every day moments. As with work samples, teachers can share their observation evidence with the children. Children are fascinated with seeing and hearing themselves. This type of documentation provides the most authentic evidence of all the observation methods.
Collecting your data
There are numerous ways to incorporate technology into your classroom. It is important to keep in mind that each early care and education program would have their own protocol, policies and procedures regarding the use of technology to document children’s learning, growth and development, so be sure to verify what you can and cannot do. Here are a few suggestions that you may want to incorporate:
Use a camera, laptop, tablet, or smartphone to record observations and take pictures
Ask a child to dictate a story and you can type it up on a computer or use an audio recorder
Scan or make copies of children’s work, such as drawings or writing, to create a visual timeline that shows a child's skill development over time.
Use email or a parent communication app to post work samples
Use voice-to-text software to document important discussions. For example, children can explain how they created their piece of art.
Take pictures of three-dimensional work. For example, woodworking projects, block towers, sandcastles, and culinary creations.
Film dramatic plays and musical performances that the children produce.
Use a video camera to document how children are progressing with their developmental milestones in each of the domains. For example, look at playful interactions to track social-emotional development; watch children on the playground to track physical development; observe how children tackle science or math activities to track cognitive development.
[31]
Organizing your data
Observation data can be conveniently stored on a computer and each child can have their own digital portfolio or file folder. For every child, you would include photos of them at play, photos of their work samples, and any audio recordings or video clips that you may have collected (as suggested above). When using smartphones to take photos or videos, you can easily upload information to your computer or transfer information to other devices. Some teachers may want to use an app to formally organize observation evidence, and some schools may purchase a program that links families to daily observations. Some centers may even use an electronic assessment program (e.g. the Desired Results Developmental Program - DRDP) to track children’s developmental progress and teachers would regularly upload observation evidence as part of the assessment process. Here are a few added suggestions on how you can organize and use stored electronic observation evidence:
Photos can be scanned, printed and posted in the classroom
A photo slideshow can be created for family nights or as a screen saver
The children can watch a video montage of a themed project they completed
Children can look at “old” photos to monitor their own developmental progress and can make comments regarding their work, their thought process and their developmental outcomes.
[32]
Table \(\PageIndex{6}\): Advantages and Disadvantages of Technology
Advantages
Disadvantages
Provides tangible/ visible evidence that teachers can use to track a child’s learning, growth and development over time
Parents and children both enjoy seeing the work on display
Captures authentic documentation which is ideal for assessment
Teachers can use information to plan and adjust curriculum to help children achieve their learning goals
Families can see how children learn through play
Children can share their insights as to
how
they created the work sample and offer their perspectives as to
what
they were thinking (authentic evidence)
Children enjoy seeing their work on
display and they can feel empowered when their work is valued
With using multi -media, children can be observed in their natural settings
Can be time consuming adding anecdotal documentation and creating documentation boards
Requires ample storage space
Requires a financial investment in technology (camera, video or audio recorder)
Concerns over confidentiality and privacy when using photos, audio or videos