One way to use degrees of certitude

Reading Prof. Gardner-Medwin comments (here) it obviously appears that my point of view needed some clarification. The way I use degrees of certitude will be described in this post. It is only one way, not pretending to be the best, just my way. Since degrees of certitude (or degrees of certainty) do not influence the mark it is not de facto a confidence based marking system.

Students are free to associate degrees of certitude with their answers. If they don’t use degree of certitude or if they use them being wrong or being right their score will not change. They answer MCQ choosing one out of 7 to 8 propositions, 4 being always the same: none of the proposition, all propositions together, missing data to answer the question, the question doesn’t make sense. The tariff is

• for a correct answer: +1
• for an incorrect answer: -0.5
• for not answering or omission: -0.25

Training a) to answer this kind of MCQ, b) to use degrees of certitude and c) specific training regarding the topics evaluated with these tests are organised, both on line and during simulated exams. Students are free to participate. If not using CBM they receive their scores. Students using CBM for all their answers receive detailed results. They connect to the web and using their student identity number they download their full results.

On a willing base they can answer 20 questions about their performance helping them to analyse their results and regulate their learning for the next test.

Five tests are organised during the year. None is mandatory. Student are free not to participate to any and only take the final oral exam.

1. The first lesson in September is a test about prerequisite knowledge.
2. The second test in December is a formative training test with MCQ and open ended questions covering all subjects seen at the point of the formation.
3. The third test in January is a summative test that will influence the final score if the test is taken. It is the same kind of test than the previous.
4. The fourth test in Ferburay is a formative evaluation covering all subjects of the year course.
5. The fifth test in March is a summative test covering all subjects of the year course.

 

The first summative test, if taken, will count for 15% of the final score. The second summative test, if taken, will count for 35% of the final score. The oral exam in June will take the remaining percentage, meaning

• 100% if no test was taken during the year,
• 85% if the first summative test was taken,
• 65% if the second summative test was taken,
• 50% if both summative test were taken.

If a student pass both summative tests with a score above 60% he then can choose

1. to take the oral exam for 50% of the final score.
2. to report his score to the oral exam so that his grade for both summative tests will be his final grade.

Any student who has not taken both test or not passed with 60% or more is obliged to take the oral exam. Any student who has taken all 5 tests and reached a score between 45% and 60% will be evaluated on the quality of his comments. If metacognitive analysis and regulations are “good” bonus points will be added to the student actual score. The bonus points allow the student to reach the 60% needed to be able to keep his grade and not being obliged to take the oral exam.

It is a long explanation. Let’s hope it makes things easier to understand. Next post will present the tool the help student to analyse and regulated their learning using results collected with the use of CBM.

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).