Definition of confidence

Another word from the 14th century. As a noun it covers different meanings like: 

• a feeling or consciousness of one’s powers or of reliance on one’s circumstances; faith or belief that one will act in a right, proper, or effective way 
• a relation of trust or intimacy; reliance on another’s discretion; support especially in a legislative body
• the quality or state of being certain 

 The last definition is the one related to the subject of confidence marking. The same words are found in the The American Heritage® Dictionary of the English Language, 4th Edition (retrieved October 26, 2007, from Dictionary.com website), the Merriam-Webster Online dictionary (retrieved October 26, 2007) and the FreeDictionary: which add to the state or quality of being certain the notion of freedom from doubt.

• Synonyms most often cited: confidence, assurance, aplomb, self-confidence, self-possession. These nouns denote a feeling of emotional security resulting from faith in oneself. 
• The Merriam-Webster adds: a state of mind or a manner marked by easy coolness and freedom from uncertainty, diffidence, or embarrassement.
  • confidence stresses faith in oneself and one’s powers without any suggestion of conceit or arrogance <the confidence that comes from long experience>. 
  • assurance carries a stronger implication of certainty and may suggest arrogance or lack of objectivity in assessing one’s own powers <handled the cross-examination with complete assurance>. 
  • self-possession implies an ease or coolness under stress that reflects perfect self-control and command of one’s powers <answered the insolent question with complete self-possession>. 
  • aplomb implies a manifest self-possession in trying or challenging situations <handled the reporters with great aplomb>.

Regarding confidence marking the meaning of confidence definetelly recovers the state or quality of being certain. But the difference between confidence and assurance is to be remembered because of the relation between assurance and certainty.

Definition of certainty

Introduction

This is not a “new pedagogical” word. It has been used for a long time, 14th century. The word is coming from certain (13th century), from Latin certus, from past participle of cernere: to sift, discern, decide; akin to Greek krinein to separate, decide, judge. Its meaning is related to fixed, settled, dependable, reliable, known or proved to be true, indisputable, assured in mind or action. 

Defintions

Several definitions exist on the web like

• Something that is clearly established or assured (from the The American Heritage® Dictionary of the English Language, Fourth Edition copyright ©2000 by Houghton Mifflin Company. Updated in 2003. Published by Houghton Mifflin Company.)
• Something that is certain. The quality or state of being certain especially on the basis of evidence. (Merriam-Webster Online dictionary, last consulted on 25th oct 2007)
• Synonyms from the Merriam-Webster online dictionary: certainty, certitude, conviction mean a state of being free from doubt.
  • certainty and certitude are very close; 
  • certainty may stress the existence of objective proof <claims that cannot be confirmed with scientific certainty>, while 
  • certitude may emphasize a faith in something not needing or not capable of proof <believes with certitude in an afterlife>. 
  • conviction applies especially to belief strongly held by an individual <holds firm convictions on every issue>.
• Synonyms from the Freedictionary: certainty, certitude, assurance, conviction : These nouns mean freedom from doubt. 
  • Certainty implies a thorough consideration of evidence: “the emphasis of a certainty that is not impaired by any shade of doubt” Mark Twain.
  • Certitude is based more on personal belief than on objective facts: “Certitude is not the test of certainty” Oliver Wendell Holmes, Jr.
  • Assurance is a feeling of confidence resulting from subjective experience: “There is no such thing as absolute certainty, but there is assurance sufficient for the purposes of human life” John Stuart Mill.
  • Conviction arises from the vanquishing of doubt: “His religion . . . was substantial and concrete, made up of good, hard convictions and opinions.” Willa Cather.
• Certainty is not defined in information theory. However, Claude Shannon, the inventor of the information theory,  discovered that uncertainty can be measured . Uncertainty is a logarithmic measure of the average number of choices that a receiver or a molecular machine like a human being has available. The best measure for certainty is a decrease of uncertainty, and this is Shannon’s information measure. The uncertainty before an event less the uncertainty after the event (equivocation) is the information.
  
• There is also a “Legal” definition: Moral certainty is the conclusion which can be arrived after considering the evidence available that the defended is guilty of the crime. Moral certainty is the state of belief one can arrive after applying a reasonable doubt on the matter under consideration.

The Freedictionary provides words in relation with certainty

• cognitive state, state of mind – the state of a person’s cognitive processes.
• confidence, self-assurance, self-confidence, sureness, assurance, authority – freedom from doubt; belief in yourself and your abilities; “his assurance in his superiority did not make him popular”; “after that failure he lost his confidence”; “she spoke with authority”.
• certitude, cocksureness, overconfidence – total certainty or greater certainty than circumstances warrant.
• reliance, trust – certainty based on past experience; “he wrote the paper with considerable reliance on the work of other scientists”; “he put more trust in his own two legs than in the gun”.
• doubt, doubtfulness, dubiety, dubiousness, incertitude, uncertainty – the state of being unsure of something.

Words like realism, sure, imprudence and prudence should also be related to the notion of certainty. 

Conclusions 

• Definition of certainty is something that is clearly established, assured, leaving no place for doubt. But as Bertrant Russel stated in 1912: “Is THERE ANY KNOWLEDGE in the world which is so certain that no reasonable man could doubt it?  ” (Russell, B. (1988) The Problems of Philosophy, Prometheus Books. Page 1). 
• It so appears that “Degree of certitude” is more what is mesured when asking the level of confidence in a given answer. This is actually the expression used in French (Degré de certitude).

Confidence weighting or Certainty Marking?

or from confidence weighting to certainty-based marking

In a previous post Robert Ebel’s definition of confidence weighting was presented: answers are associated with certainty of the answer correctness. Ebel uses weighting which in his definition is associated with a mode of scoring. Gardner-Medwin (see the post here) uses marking, which is related to words like evaluation, grade. Because of the use of “marking” both confidence or certainty are associated with a mark scheme.

Ebel’s objectives for using confidence weighting are related to minimize score by guessing (“to reduce the chance error component on a test score”).

Gardner-Medwin’s objectives range

• from “risk losing marks if wrong” which is related to words like tariff, mark scheme, reckoner,…
• to “think about how reliable your answer” which is related to metacognitive judgment.

I’ve already mentioned that it is my opinion that in evaluation, degrees of certainty can be successfully used without being associated with reckoner or tariff. But I must add that mark scheme might interfere with honest expression of confidence using degree of certainty. In a survey on 349 students, 52% admitted that the were using one specific strategy, some always, some time to time, to choose the degree of certainty given with an answer instead of giving an honest expression of how reliable the chosen answer was. This survey, with other facts, suggests that using degree of certainty with a mark scheme might bias the honest expression of confidence or doubt associated with an answer.

Depending of the objectives linked with the use of degree of certainty a careful choice must be made regarding he fact of using or not using a mark scheme, tariff or reckoner because of possible bias using a strategy to answer instead of honest expression of confidence.