definition of terms

A main idea
- is important information that tells more about the overall idea of a paragraph or section of a text.

- The main idea is the most important thing the paragraph says about the topic. The topic is what a paragraph is all about.

CONTEXT CLUES
- are hints that the author gives to help define a difficult or unusual word. The clue may appear within the same sentence as the word to which it refers, or it may be in a preceding or subsequent sentence. Because most of your vocabulary is gained through reading, it is important that you be able to recognize and take advantage of context clues.

Types of context clues. There are at least four kinds of context clues that are quite common.

Synonym
A synonym, or word with the same meaning, is used in the sentence.
My opponent's argument is fallacious, misleading – plain wrong.

Antonym
A word or group of words that has the opposite meaning reveals the meaning of an unknown term.
Although some men are loquacious, others hardly talk at all.

Explanation
The unknown word is explained within the sentence or in a sentence immediately preceding.
The patient is so somnolent that she requires medication to help her stay awake for more than a short time.

Example
Specific examples are used to define the term.
Celestial bodies, such as the sun, moon, and stars, are governed by predictable laws.
Read the following sentences and define the bolded word based on the context clue. Then identify which of the four types of clues is used.
1.
The girl who used to be very vociferous doesn't talk much anymore.
2.
Pedagogical institutions, including high schools, kindergartens, and colleges, require community support to function efficiently.
3.
He was so parsimonious that he refused to give his own sons the few pennies they needed to buy pencils for school. It truly hurt him to part with his money.
4.
His pertinacity, or stubbornness, is the cause of most of his trouble.
5.
Rather than be involved in clandestine meetings, they did everything quite openly.
6.
Ecclesiastics, such as priests, ministers, and pastors, should set models of behavior for their congregants.
7.
The girl was churlish – rude, sullen and absolutely ill-mannered.
8.
Because the conflagration was aided by wind, it was so destructive that every building in the area was completely burned to the ground.
Joffe, Irwin L. Opportunity for Successful Reading, 8th ed. Belmont: Wadsworth, 1997.

ANSWER KEY TO CONTEXT CLUES HANDOUT
1.
Type of Context Clue–antonymdefinition of vociferous–talkative; outspoken
2.
Type of Context Clue–example definition of pedagogical–having to do with teaching
3.
Type of Context Clue–explanation definition of parsimonious–stingy; tightfisted
4.
Type of Context Clue–synonym definition of pertinacity–mulish; stubborn
5.
Type of Context Clue–antonymdefinition of clandestine–secret; hidden
6.
Type of Context Clue–example definition of ecclesiastics–member of the clergy
7.
Type of Context Clue–synonymdefinition of sullen–rude
8.
Type of Context Clue–explanation definition of conflagration–fire

Cause and effect
- refers to the philosophical concept of causality.

Compare and contrast
- To set in opposition, or over against, in order to show the differences between, or the comparative excellences and defects of; to compare by difference or contrariety of qualities; as, to contrast the present with the past.


The supporting details
- give more information about the topic. They are not as general as the main idea. Instead, they help the reader understand more about the main idea.

Raise Your Academic Performance

Academic knowledge gets you ahead in a competitive world.

Academic performance really means three things: The ability to study and remember facts, being able to study effectively and see how facts fit together and form larger patterns of knowledge and being able to think for yourself in relation to facts and thirdly being able to communicate your knowledge verbally or down on paper.

Good academic performance is also linked having good organizational skills such as a tidy place to work and good time management. And these are all things you need to consider.

But this 'raise your academic performance' session focuses and concentrates on you having the right mind-set for raising your academic performance so you can learn more effectively. When you relax then your mind becomes more absorbent and able to learn.

You also need confidence that you can be smarter and have faith that your perceptions and ides are as good as if not better than many other people's.

definition of terms

word problem (mathematics education) is a type of textbook problem designed to help students apply abstract mathematical concepts to "real-world" situations

ability -
1.The quality of being able to do something, especially the physical, mental, financial, or legal power to accomplish something.
2. A natural or acquired skill or talent.

Math and Problem Solving Skills
Mathematics GradesProblem solving is the foundation of math and a necessary skill for good grades in math. For children to learn problems solving skills, they need personal connections. Improve When Understanding How to Solve Problems
© David R. Wetzel
Problem Solving in Math is Personal
The ability to solve problems is the foundation of mathematics. For a student in any grade in school, the road to understanding math is through the problem solving gateway. This is not to be confused with completing worksheets; these are real world personal problems which require logical thinking and reasoning skills to solve.

Problem solving is the foundation of math and a necessary skill for good grades in math. For children to learn problems solving skills, they need personal connections.

Solving problems is one of the most challenging math skills to learn. Inefficiency in solving math problems holds many people back from rewarding academic and technical careers. Building problem solving skills requires grasping math concepts and a large amount of training in solving math tasks

Theories about problem solving

Theories of problem-solving are dominated by the work of Newell & Simon on GPS (General Problem Solver). This work established the information processing paradigm for the study of problem-solving and the concepts of "means-ends-analysis" and "problem space". According to the GPS framework, problem-solving involves the identification of subgoals and the use of methods (especially heuristics) to satisfy the subgoals.


The Gestalt psychologist Wertheimer also conducted research on problem-solving and emphasized the importance of understanding the structure (i.e., the relationship among parts) of the problem. In his lateral thinking theory, DeBono stressed the importance of looking at a problem with a fresh perspective.


Schoenfeld presents a theory of problem-solving in mathematics that involves four aspects: resources, heuristics, control, and beliefs. Although this framework was specifically developed for mathematical problem-solving, it seems more generally applicable. Bransford et al. present a problem-solving approach to the use of hypermedia in their anchored instructional theory.


Problem-solving skills appear to be related to many other aspects of cognition (Frederiksen, 1984) such as schema (the ability to remember similar problems), pattern recognition (recognizing familiar problem elements) and creativity (developing new solutions). The issue of transfer is highly relevant to problem solving. A good summary of problem-solving research as it applies to instruction is provided by Tuma & Rief (1980). Problem-solving skills are fundamental to many professional domains such as engineering or medicine.

Problem-solving

A problem is a situation which is experienced by an agent as different from the situation which the agent ideally would like to be in. A problem is solved by a sequence of actions that reduce the difference between the initial situation and the goal.

A problem can be analysed into more specific components. First of all it consists of the two situations, the present one which we will call the initial state, and the desired one, which we can call the goal state. The agent's task is to get from the initial state to the goal state by means of series of actions that change the state. The problem is solved if such a series of actions has been found, and the goal has been reached. In general, problem-solving is a component of goal-directed action or control.


In simple control problems, the solution is trivial. For example, the thermostat is a control system or agent whose goal is to reach or maintain a specific temperature. The initial state is the present temperature. The action consists in either heating to increase the temperature or cooling to decrease it. The decision which of these two possible actions to apply is trivial: if the initial temperature is lower than the goal temperature, then heat; if it is higher, then cool; if it is the same, then do nothing. Such problems are solved by a deterministic algorithm: at every decision point there is only one correct choice. This choice is guaranteed to bring the agent to the desired solution.


The situations we usually call "problems" have a more complex structure. There is choice of possible actions, none of which is obviously the right one. The most general approach to tackle such processes is generate and test: apply an action to generate a new state, then test whether the state is the goal state; if it is not, then repeat the procedure. This principle is equivalent to trial-and-error, or to evolution's variation and selection. The repeated application of generate and test determines a search process, exploring different possibilities until the goal is found. Searches can be short or long depending on the complexity of the problem and the efficiency of the agent's problem-solving strategy or heuristic. Searches may in fact be infinitely long: even if a solution exists, there is no guarantee that the agent will find it in a finite time.


Such a search process requires a series of actions, carefully selected from a repertoire of available actions to bring the present state closer to the goal. Different actions will have different effects on the state. Some of these effects will bring the present state closer to the goal, others will rather push it farther away. To choose the best action at every moments of the problem-solving process, the agent needs some knowledge of the problem domain. This knowledge will have the general form of a production rule: if the present state has certain properties, then perform a certain action. Such heuristic knowledge requires that the problem states be distinguished by their properties. This leads us to a further analysis of problems.


Problem states will generally involve objects, which are the elements of the situation that are invariant under actions, and properties or predicates, which are the variable attributes of the objects. A problem state then can be formulated as a combination of propositions, where elementary propositions attribute a particular predicate to a particular object. The different values of the predicates determine a set of possible propositions, and thus of possible states. Since states that differ only in one value of one predicate can be said to be "closer" together than states that differ in several values, the state set gets the structure of a space, ordered by an elementary "distance" function. Actions can now be represented as operators or transformations, which map one element of the state space onto another, usually neighbouring, element.


The final component we need to decide between actions is a selection criterion, which tells the agent which of the several actions that can be applied to a given state is most likely to bring it closer to the goal. In the simplest case, an action consists simply of moving to one of the neighbouring states. Each state will then be associated with a certain value which designates the degree to which it satisfies the goal. This value may be called "fitness". The search space then turns into a fitness landscape, where every point in the space ("horizontal") is associated with a "vertical" fitness value, so that a landscape with valleys and peaks appears. Problem-solving then reduces to "hill-climbing": following the path through the fitness landscape that leads most directly upward.


The efficiency of problem-solving is strongly determined by the way the problem is analysed into separate components: objects, predicates, state space, operators, selection criteria. This is called the problem representation. Changing the problem representation, i.e. analysing the problem domain according to different dimensions or distinctions, is likely to make the problem much easier or much more difficult to solve. States which are near to each other in one representation may be far apart in another representation of the same problem. Therefore, a goal state that could be reached easily in one representation may be virtually impossible to find in another one. Problem representations are usually also models of the situation as experienced by the agent.

Problem solving

Problem solving forms part of thinking. Considered the most complex of all intellectual functions, problem solving has been defined as higher-order cognitive process that requires the modulation and control of more routine or fundamental skills (Goldstein & Levin, 1987). It occurs if an organism or an artificial intelligence system does not know how to proceed from a given state to a desired goal state. It is part of the larger problem process that includes problem finding and problem shaping.The nature of human problem solving methods has been studied by psychologists over the past hundred years. There are several methods of studying problem solving, including; introspection, behaviorism, simulation and computer modeling, and experiment.


Beginning with the early experimental work of the Gestaltists in Germany (e.g. Duncker, 1935), and continuing through the 1960s and early 1970s, research on problem solving typically conducted relatively simple, laboratory tasks (e.g. Duncker's "X-ray" problem; Ewert & Lambert's 1932 "disk" problem, later known as Tower of Hanoi) that appeared novel to participants (e.g. Mayer, 1992). Various reasons account for the choice of simple novel tasks: they had clearly defined optimal solutions, they were solvable within a relatively short time frame, researchers could trace participants' problem-solving steps, and so on. The researchers made the underlying assumption, of course, that simple tasks such as the Tower of Hanoi captured the main properties of "real world" problems, and that the cognitive processes underlying participants' attempts to solve simple problems were representative of the processes engaged in when solving "real world" problems. Thus researchers used simple problems for reasons of convenience, and thought generalizations to more complex problems would become possible. Perhaps the best-known and most impressive example of this line of research remains the work by Newell and Simon (1972).

Finding the Main idea

You are on your way to AmLa class, and your friend asks you about the movie you saw last night. Your friend doesn't have time to hear about the whole two hours of the movie, but you can tell you friend in a few sentences what the movie is about.
What's it all about?
The answer to this question is the main idea. The Main idea refers to what a paragraph or an article is about. "Main" means what is important, or key, the heart of the matter. "Idea" means the thought, the thesis or the topic.

Finding the Main Idea
In English paragraphs, the Main Idea will most likely be found in one of these five places:
in the first sentence
in the last sentence
in the middle of the paragraph
in two sentences of the paragraph
not stated in the paragraph directly (implied)

Read the following paragraphs and tell where the main idea is located.
A. Despite the hatred that most people feel toward cockroaches, they do help humans in several ways. For example, they are perfect experimental animals and are used for scientific research in the laboratory. Breeding them is easy, for they thrive under almost any conditions. In studies on nutrition and food, cockroaches are good subjects because they will eat any kind of food. They can be used to study heart disease, and cancer researchers work with roaches because they grow cancerous tumors like those that are found in humans.
1) in the first sentence2) in the last sentence3) in the middle of the paragraph4) in two sentences of the paragraph5) not stated in the paragraph directly (implied)
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Answer 1) In the first sentence

B. About 300 million years ago, long before dinosaurs ruled the earth, the cockroach already had been here for a long time. We can only guess at why it has not become extinct, but the physical assets of the cockroach provide a major reason for its survival. The cockroach's body is very flat, allowing it to slip into tiny cracks and crevices, and its six strong running legs give it unmatched powers of escape. Two small feelers detect movements and changes in air currents, thus warning the insect of approaching danger. The cockroach's two large eyes are made up of hundreds of tiny, separate eyes which are very good for seeing movements - an ability that helps a roach escape its enemies.
1) in the first sentence2) in the last sentence3) in the middle of the paragraph4) in two sentences of the paragraph5) not stated in the paragraph directly (implied)
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Answer 4) In two sentences

C. Making a study schedule is one important step in becoming a successful student in college. Students should schedule one hour of study time for every one hour of class time. At exam time, more study time may be necessary. Also, students must study in an appropriate place. It is important to study in a quiet place away from the distraction of other people and such things as the television and the radio. Students should find a comfortable place with plenty of space for all the necessary study supplies. Then, students need to study the information in small amounts. It is a good idea to learn the required concepts slowly and thoroughly instead of trying to learn everything on the evening before the exam. Students who want to be successful in college should remember these three helpful study strategies.
1) in the first sentence2) in the last sentence3) in the middle of the paragraph4) in two sentences of the paragraph5) not stated in the paragraph directly (implied)
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Answer 4) in the last sentence

D. Every game from the latest multimedia games to old favorites like cards and chess can be played on home computers. Home computers are used to balance family finances, to complete banking transactions, and even to do the grocery shopping. Those computers which are equipped with a modem allow users to go "online" to "chat" with others -- that is, people can have a conversation on the computer about anything from being in love to getting medical advice. And of course students use home computers to type up school reports, to research their papers for classes and even to do the calculations for math homework.
1) in the first sentence2) in the last sentence3) in the middle of the paragraph4) in two sentences of the paragraph5) not stated in the paragraph directly (implied)
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Answer 5) It is implied: MIS = Computers have many uses today.

E. Television can be an excellent teacher for everyone from very young children to the oldest of viewers. Television entertains young children with sights and songs. Television provides company for older viewers who are stuck at home with no one to talk to. New immigrants can learn English just by turning on the television. All viewers can keep informed on the latest events around the world by watching the news. While there are many great things about television, there are also many bad things. Over time, television shows have begun to show more and more violence, death and murder. The bad language and profanity on some shows make them unsuitable for families. The number of shows which deal with sex outside of marriage also shocks many viewers. And these terrible scenes are sometimes copied by young, impressionable viewers.
1) in the first sentence2) in the last sentence3) in the middle of the paragraph4) in two sentences of the paragraph5) not stated in the paragraph directly (implied)
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Answer 3) in the middle of the paragraph

Answering Questions about the Main Idea
You can now determine where the Main Idea is located within a paragraph. Once you can identify where the main idea is, you can move on to the next step -- showing that you understand what the main idea is, or telling what the paragraph or article is about. If you can talk or write about the main idea, then it is clear that you have understood what you have read.

There are usually two types of main idea questions:
(1) multiple choice questions: you are given four or five choices and must choose the best main idea statement.
First identify the sentence that best states the main idea.
Then choose the statement from the answer choices that is closest in meaning to the sentence that you think is the main idea.

Read this paragraph. Then answer the quetsions.
Southern California is known for its tourist attractions and its theme parks. People come from all over the world to get a look at Hollywood, and such things as the "Walk of Fame" where many celebrities’ names are found on gold stars on Hollywood Boulevard. Tourists are also attracted to the area with hopes of catching sight of the movie stars who live in the hills surrounding Los Angeles. Many visitors come to shop in the glamorous shops on Rodeo Drive in Beverly Hills. Among the theme parks that attract visitors are Disneyland in Anaheim, Knott’s Berry Farm, Magic Mountain Amusement Park, and Raging Waters park. Folks who want to combine tourist attractions and theme parks can visit Universal Studios which offers both.
1. First identify the sentence where the main idea is located.
in the first sentence
in the last sentence
in the middle of the paragraph
in two sentences of the paragraph
not stated in the paragraph directly (implied)
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Answer 1) in the first sentence
2. Which of the following statements best states the main idea of this passage?
a. Disneyland is famous all over the world.
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If you chose answer "a" then you have selected an answer which tells one detail from the paragraph. This is not a sentence of what the whole paragraph is about, so it is not a statement of the main idea of the paragraph.
b. Have you ever been to Southern California? b. Have you ever been to Southern California?
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There are actually two problems with this answer. First, the main idea is rarely stated in the form of a question. When you write your own main idea statement, do not write a question. Second, this question is much too general. Southern California, by itself, is too large to be the topic. What does the paragraph tell the reader about Southern California? Is it about the beaches? The weather? The traffic problems? This question is too general because it does not give specific information about this topic.
c. Most tourists enjoy Southern California. c. Most tourists enjoy Southern California.
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You have the right idea, but the wrong answer. Tourists probably do enjoy Southern California, but the paragraph tells the reader more specifically about two things that tourists enjoy in Southern California. This statement by itself is too general. It does not tell the reader exactly what tourists enjoy in Southern California.
d. Southern California has both tourist attractions and theme parks for visitors. d. Southern California has both tourist attractions and theme parks for visitors.
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This paragraph tells the reader about two things that visitors enjoy in Southern California, the tourist attractions and the theme parks, so this statement is the best main idea statement. You are right. Good Job!
e. Many movie stars live in the Southern California area. e. Many movie stars live in the Southern California area.
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You have chosen one detail from this paragraph, but this does not tell the reader what the whole paragraph is about. While it may be true that many movie stars live in Southern California, the paragraph gives us a lot of information besides this one fact.
(2) writing questions: you are asked to write a sentence to state the main idea in your own words.
This question asks you to state the main idea in "your own sentence."
This means that you cannot copy a sentence that has already been written by someone else, including a sentence from the paragraph.

A main idea sentence has two parts, usually called the topic and the controlling idea. If you like math, think of it as an equation:
MIS = T + CI

Read this paragraph. Then answer the questions that follow.
Dogs are good for children because they teach children to be responsible. Children who have to feed the dog, give the dog water, and to walk the dog learn to be responsible for the life of another being. Cats also teach children responsibility, and along with this, children who own a cat learn about independence since cats are quick to teach this. Rabbits teach children about having babies because as anyone who has owned more than one rabbit knows, they have a lot of babies. Snakes, rats, fish and gerbils are also good to teach children about cleanliness and proper bathing habits. Most pets teach children valuable lessons.
1. First identify the sentence where the main idea is located.
in the first sentence
in the middle of the paragraph
in the last sentence
in two sentences of the paragraph
not stated in the paragraph directly (implied)
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Answer in the last sentence
Think of your own sentence to state the main idea of this paragraph.

Did you copy the last sentence from the paragraph?
If you did, then you would not get credit for writing your own sentence. This question asks you to state the main idea in "your own sentence." This means that you cannot copy a sentence that has already been written by someone else.

Did you write a sentence with the word "pets" in it?
If you did, then you have at least part of the answer correct.
Remember: MIS = T + CI

In this example paragraph, the topic is pets.
The topic is who or what the paragraph is about.
The controlling idea is that pets can be good teachers for children, or that pets can teach children many things.

The controlling idea is what we learn, or what we find out in this paragraph about the topic.
After you decide who are what the paragraph is about (the topic), ask yourself, "What is the writer telling me about this topic?" The answer to this question is the controlling idea.

There is more than one way to state the controlling idea, so if you compare your main idea sentence to someone else’s you may not have the exact same sentence. But, if you both understood the paragraph, you should have sentences which are similar.

Inference

Inference is the act or process of deriving a conclusion based solely on what one knows.

Inference is studied within several different fields.

Human inference (i.e. how humans draw conclusions) is traditionally studied within the field of cognitive psychology.

Logic studies the laws of valid inference.

Statisticians have developed formal rules for inference (statistical inference) from quantitative data.

Artificial intelligence researchers develop automated inference systems.
Contents[hide]

1 The accuracy of inductive and deductive inferences
1.1 Inductive
2 Headline text'''Insert non-formatted text here'''IM GOIN TO GUT U LIKE A FISH!!
2.1 Deductive
3 Valid inferences
4 Examples of deductive inference
5 Incorrect inference
6 Automatic logical inference
6.1 An example: inference using Prolog
6.2 Automatic inference and the semantic web
7 Inference and uncertainty
7.1 Bayesian statistics and probability logic
7.2 Nonmonotonic logic
8 Three types of logical inference
8.1 An example
9 See also
10 References
//

The accuracy of inductive and deductive inferences

Inductive
The process by which a conclusion is inferred from multiple observations is called inductive reasoning. The conclusion may be correct or incorrect, or partially correct, or correct to within a certain degree of accuracy, or correct in certain situations. Conclusions inferred from multiple observations may be tested by additional observations.

Headline text'''Insert non-formatted text here'''IM GOIN TO GUT U LIKE A FISH!!
Inductive inference is the method of science. A theory is proposed based on multiple observations, usually observations carried out with great care, using measurement. The theory is then tested many times, by independent investigators, using their own multiple observations. If the theory proves correct to within the accuracy of those observations, then it is provisionally accepted. Any scientific theory is subject to additional testing, and may be modified or overthrown based on additional evidence. For example, the Germ Theory of Disease required modification when viruses and also deficiency diseases were discovered.
Scientific theories arrived at by inductive inference have proved stable enough over long periods of time to revolutionize the way human beings live. A scientific theory can be overthrown only by carefully recorded repeated observations, carried out independently by a large number of investigators. They cannot be overthrown by revelation, authority, ignorance, or doubt.[1]

Deductive
The process by which a conclusion is logically inferred from certain premises is called deductive reasoning. Deductive inference is the method of mathematics. Certain definitions and axioms are taken as a starting point, and from these certain theorems are deduced using pure reasoning. The idea for a theorem may have many sources: analogy, pattern recognition, and experiment are examples of where the inspiration for a theorem comes from. However, a conjecture is not granted the status of theorem until it has a deductive proof. This method of inference is even more accurate than the scientific method. Mistakes are usually quickly detected by other mathematicians and corrected. The proofs of Euclid, for example, have mistakes in them that have been caught and corrected, but the theorems of Euclid, all of them without exception, have stood the test of time for more than two thousand years.[2]
From a pragmatic viewpoint, the inferences arrived at by the methods of science and mathematics have proved much more successful than the inferences arrived at by any other method. This has given rise to the popular saying, when a conclusion is challenged, "Do the math."

Valid inferences
Inferences are either valid or invalid, but not both. Philosophical logic has attempted to define the rules of proper inference, i.e. the formal rules that, when correctly applied to true premises, lead to true conclusions. Aristotle has given one of the most famous statements of those rules in his Organon. Modern mathematical logic, beginning in the 19th century, has built numerous formal systems that embody Aristotelian logic (or variants thereof).
Examples of deductive inference
Greek philosophers defined a number of syllogisms, correct three-part inferences, that can be used as building blocks for more complex reasoning. We'll begin with the most famous of them all:All men are mortal
Socrates is a man
------------------
Therefore Socrates is mortal.
The reader can check that the premises and conclusion are true. The Latin name for this form was modus ponens.
The validity of an inference depends on the form of the inference. That is, the word "valid" does not refer to the truth of the premises or the conclusion, but rather to the form of the inference. An inference can be valid even if the parts are false, and can be invalid even if the parts are true. But a valid form with true premises will always have a true conclusion.
For example, consider the form of Modus Ponens:All A are B
C is A
----------
Therefore C is B
The form remains valid even if all three parts are false:All apples are blue.
A banana is an apple.
----
Therefore bananas are blue.
For the conclusion to be necessarily true, the premises need to be true.
Now we turn to an invalid form.All A are B.
C is a B.
----
Therefore C is an A.
To show that this form is invalid, we demonstrate how it can lead from true premises to a false conclusion.All apples are fruit. (true)
Bananas are fruit. (true)
----
Therefore bananas are apples. (false)
A valid argument with false premises may lead to a false conclusion:All fat people are Greek
John Lennon was fat
-------------------
Therefore John Lennon was Greek
where a valid argument is used to derive a false conclusion from false premises. The inference is valid because it follows the form of a correct inference.
A valid argument can also be used to derive a true conclusion from false premises:All fat people are musicians
John Lennon was fat
-------------------
Therefore John Lennon was a musician
In this case we have two false premises that imply a true conclusion.

Incorrect inference
An incorrect inference is known as a fallacy. Philosophers who study informal logic have compiled large lists of them, and cognitive psychologists have documented many biases in human reasoning that favor incorrect reasoning.

Automatic logical inference
AI systems first provided automated logical inference and these were once extremely popular research topics, leading to industrial applications under the form of expert systems and later business rule engines.
An inference system's job is to extend a knowledge base automatically. The knowledge base (KB) is a set of propositions that represent what the system knows about the world. Several techniques can be used by that system to extend KB by means of valid inferences. An additional requirement is that the conclusions the system arrives at are relevant to its task.

An example: inference using Prolog
Prolog (for "Programming in Logic") is a programming language based on a subset of predicate calculus. Its main job is to check whether a certain proposition can be inferred from a KB (knowledge base) using an algorithm called backward chaining.
Let us return to our Socrates syllogism. We enter into our Knowledge Base the following piece of code:mortal(X) :- man(X).
man(socrates).
( Here :- can be read as if. Generally, if P Q (if P then Q) then in Prolog we would code Q:-P (Q if P).)This states that all men are mortal and that Socrates is a man. Now we can ask the Prolog system about Socrates:?- mortal(socrates).
(where ?- signifies a query: Can mortal(socrates). be deduced from the KB using the rules) gives the answer "Yes".
On the other hand, asking the Prolog system the following:?- mortal(plato).
gives the answer "No".
This is because Prolog does not know anything about Plato, and hence defaults to any property about Plato being false (the so-called closed world assumption). Finally ?- mortal(X) (Is anything mortal) would result in "Yes" (and in some implemenations: "Yes": X=socrates)Prolog can be used for vastly more complicated inference tasks. See the corresponding article for further examples.

Automatic inference and the semantic web
Recently automatic reasoners found in semantic web a new field of application. Being based upon first-order logic, knowledge expressed using one variant of OWL can be logically processed, i.e., inference can be made upon it.

Inference and uncertainty

This article needs additional citations for verification.Please help improve this article by adding reliable references. Unsourced material may be challenged and removed. (July 2007)
Traditional logic is only concerned with certainty—one progresses from premises to a conclusion, where all the premises and the conclusion are declarative sentences that are either true or false. There are several motivations for extending logic to deal with uncertain "propositions" and weaker modes of reasoning.
Philosophical motivations
A large part of our everyday reasoning does not follow the strict rules of logic, but is nevertheless effective in many cases.
Science itself is not deductive, but largely inductive, and its process cannot be captured by standard logic (see problem of induction).
Technical motivations
Statisticians and scientists wish to be able to infer parameters or test hypothesis on statistical data in a rigorous, quantified way.
Artificial intelligence systems need to reason efficiently about uncertain quantities.
The reason most examples of applying deductive logic, such as the one above, seem artificial is because they are rarely encountered outside fields such as mathematics. Most of our everyday reasoning is of a less "pure" nature.
To take an example: suppose you live in a flat. Late at night, you are awakened by creaking sounds in the ceiling. You infer from these sounds that your neighbour upstairs is having another bout of insomnia and is pacing in his room, sleepless.
Although that reasoning seems sound, it does not fit in the logical framework described above. First, the reasoning is based on uncertain facts: what you heard were creaks, not necessarily footsteps. But even if those facts were certain, the inference is of an inductive nature: perhaps you have often heard your neighbour at night, and the best explanation you have found is that he or she is an insomniac. Hence tonight's footsteps.
It is easy to see that this line of reasoning does not necessarily lead to true conclusions: perhaps your neighbour had a very early plane to catch, which would explain the footsteps just as well. Uncertain reasoning can only find the best explanation among many alternatives.
Bayesian statistics and probability logic

Philosophers and scientists who follow the Bayesian framework for inference use the mathematical rules of probability to find this best explanation. The Bayesian view has a number of desirable features—one of them is that it embeds deductive (certain) logic as a subset (this prompts some writers to call Bayesian probability "probability logic", following E. T. Jaynes).
Bayesianists identify probabilities with degrees of beliefs, with certainly true propositions having probability 1, and certainly false propositions having probability 0. To say that "it's going to rain tomorrow" has a 0.9 probability is to say that you consider the possibility of rain tomorrow as extremely likely.
Through the rules of probability, the probability of a conclusion and of alternatives can be calculated. The best explanation is most often identified with the most probable (see Bayesian decision theory). A central rule of Bayesian inference is Bayes' theorem, which gave its name to the field.
See Bayesian inference for examples.

Nonmonotonic logic
Source: Article of André Fuhrmann about "Nonmonotonic Logic"
A relation of inference is monotonic if the addition of premisses does not undermine previously reached conclusions; otherwise the relation is nonmonotonic. Deductive inference, at least according to the canons of classical logic, is monotonic: if a conclusion is reached on the basis of a certain set of premisses, then that conclusion still holds if more premisses are added.
By contrast, everyday reasoning is mostly nonmonotonic because it involves risk: we jump to conclusions from deductively insufficient premises. We know when it is worth or even necessary (e.g. in medical diagnosis) to take the risk. Yet we are also aware that such inference is defeasible—that new information may undermine old conclusions. Various kinds of defeasible but remarkably successful inference have traditionally captured the attention of philosophers (theories of induction, Peirce’s theory of abduction, inference to the best explanation, etc.). More recently logicians have begun to approach the phenomenon from a formal point of view. The result is a large body of theories at the interface of philosophy, logic and artificial intelligence.

Three types of logical inference
There are three types of inference:
Deductive reasoning, finding the effect with the cause and the rule.
Abductive reasoning, finding the cause with the rule and the effect.
Inductive reasoning, finding the rule with the cause and the effect.

An example
Hooke's law is the rule that gives the elongation of a beam (that's an effect) when a force (that's the cause) is acting on a beam.
If the force and Hooke's law are known, the elongation of the beam can be deduced.
If the elongation and Hooke's law are known, the force acting on the beam can be abduced.
If the elongation and the force are known, Hooke's law can be induced.

See also
Reasoning
Abductive reasoning
Deductive reasoning
Inductive reasoning
Retroductive reasoning
Analogy
Axiom
Bayesian inference
Business rule
Business rules engine
Expert system
Fuzzy logic
Inference engine
Inquiry
Logic
Logic of information
Logical assertion
Logical graph
Nonmonotonic logic
Rule of inference
List of rules of inference
Theorem

SAT Prep | Introduction: Word Problems

One of the main problems students have in mathematics involves solving word problems. The secret to solving these problems is being able to convert words into numbers and variables in the form of an algebraic equation.

The easiest way to approach a word problem is to read the question and ask yourself what you are trying to find. This unknown quantity can be represented by a variable.
Next, determine how the variable relates to the other quantities in the problem. More than likely, these quantities can be explained in terms of the original variable.

Problem Solving:

Problem Solving is very important but problem solvers often misunderstand it. This report proposes the definition of problems, terminology for Problem Solving and useful Problem Solving patterns.
We should define what is the problem as the first step of Problem Solving. Yet problem solvers often forget this first step.
Further, we should recognize common terminology such as Purpose, Situation, Problem, Cause, Solvable Cause, Issue, and Solution. Even Consultants, who should be professional problem solvers, are often confused with the terminology of Problem Solving. For example, some consultants may think of issues as problems, or some of them think of problems as causes. But issues must be the proposal to solve problems and problems should be negative expressions while issues should be a positive expression. Some consultants do not mind this type of minute terminology, but clear terminology is helpful to increase the efficiency of Problem Solving. Third, there are several useful thinking patterns such as strategic thinking, emotional thinking, realistic thinking, empirical thinking and so on. The thinking pattern means how we think. So far, I recognized fourteen thinking patterns. If we choose an appropriate pattern at each step in Problem Solving, we can improve the efficiency of Problem Solving.
This report will explain the above three points such as the definition of problems, the terminology of Problem Solving, and useful thinking patterns.
Definition of problem
A problem is decided by purposes. If someone wants money and when he or she has little money, he or she has a problem. But if someone does not want money, little money is not a problem.
For example, manufacturing managers are usually evaluated with line-operation rate, which is shown as a percentage of operated hours to potential total operation hours. Therefore manufacturing managers sometimes operate lines without orders from their sales division. This operation may produce more than demand and make excessive inventories. The excessive inventories may be a problem for general managers. But for the manufacturing managers, the excessive inventories may not be a problem.
If a purpose is different between managers, they see the identical situation in different ways. One may see a problem but the others may not see the problem. Therefore, in order to identify a problem, problem solvers such as consultants must clarify the differences of purposes. But oftentimes, problem solvers frequently forget to clarify the differences of purposes and incur confusion among their problem solving projects. Therefore problem solvers should start their problem solving projects from the definition of purposes and problems
Terminology of Problem Solving
We should know the basic terminology for Problem Solving. This report proposes seven terms such as Purpose, Situation, Problem, Cause, Solvable Cause, Issue, and Solution.
Purpose
Purpose is what we want to do or what we want to be. Purpose is an easy term to understand. But problem solvers frequently forget to confirm Purpose, at the first step of Problem Solving. Without clear purposes, we can not think about problems.
Situation
Situation is just what a circumstance is. Situation is neither good nor bad. We should recognize situations objectively as much as we can. Usually almost all situations are not problems. But some problem solvers think of all situations as problems. Before we recognize a problem, we should capture situations clearly without recognizing them as problems or non-problems. Without recognizing situations objectively, Problem Solving is likely to be narrow sighted, because problem solvers recognize problems with their prejudice.
Problem
Problem is some portions of a situation, which cannot realize purposes. Since problem solvers often neglect the differences of purposes, they cannot capture the true problems. If the purpose is different, the identical situation may be a problem or may not be a problem.
Cause
Cause is what brings about a problem. Some problem solvers do not distinguish causes from problems. But since problems are some portions of a situation, problems are more general than causes are. In other words causes are more specific facts, which bring about problems. Without distinguishing causes from problems, Problem Solving can not be specific. Finding specific facts which causes problems is the essential step in Problem Solving.
Solvable Cause
Solvable cause is some portions of causes. When we solve a problem, we should focus on solvable causes. Finding solvable causes is another essential step in Problem Solving. But problem solvers frequently do not extract solvable causes among causes. If we try to solve unsolvable causes, we waste time. Extracting solvable causes is a useful step to make Problem Solving efficient.
Issue
Issue is the opposite expression of a problem. If a problem is that we do not have money, the issue is that we get money. Some problem splvers do not know what Issue is. They may think of "we do not have money" as an issue. At the worst case, they may mix the problems, which should be negative expressions, and the issues, which should be positive expressions.
Solution
Solution is a specific action to solve a problem, which is equal to a specific action to realize an issue. Some problem solvers do not break down issues into more specific actions. Issues are not solutions. Problem solvers must break down issues into specific action.
Thinking patterns
This report lists fourteen thinking patters. Problem solvers should choose appropriate patterns, responding to situations. This report categorized these fourteen patterns into three more general groups such as thinking patterns for judgements, thinking patterns for thinking processes and thinking patterns for efficient thinking. The following is the outlines of those thinking patterns.
Thinking patterns for judgements
In order to create a value through thinking we need to judge whether what we think is right or wrong. This report lists four judging patterns such as strategic thinking, emotional thinking, realistic thinking, and empirical thinking.
Strategic thinking
Focus, or bias, is the criterion for strategic thinking. If you judge whether a situation is right or wrong based on whether the situation is focused or not, your judgement is strategic. A strategy is not necessarily strategic. Historically, many strategists such as Sonfucis in ancient China, Naplon, M. Porter proposed strategic thinking when they develop strategies.
Emotional thinking
In organizations, an emotional aspect is essential. Tactical leaders judge whether a situation is right or wrong based on the participantsf emotional commitment. They think that if participants can be positive to a situation, the situation is right.
Realistic thinking
Start from what we can do
Fix the essential problem first
These two criteria are very useful. "Starting" is very important, even if we do very little. We do not have to start from the essential part. Even if we start from an easier part, starting is a better judgement than a judgement of not-starting in terms of the first part of realistic thinking. Further, after we start, we should search key factors to make the Problem Solving more efficient. Usually, 80 % of the problems are caused by only 20 % of the causes. If we can find the essential 20 % of the causes, we can fix 80 % of problems very efficiently. Then if we try to find the essential problem, what we are doing is right in terms of the second part of realistic thinking.
Empirical thinking
When we use empirical thinking, we judge whether the situation is right or wrong based on our past experiences. Sometimes, this thinking pattern persists on the past criteria too much, even if a situation has changed. But when it comes to our daily lives, situations do not change frequently. Further, if we have the experience of the identical situation before, we can utilize the experience as a reliable knowledge data base.
Thinking patterns for thinking processes
If we can think systematically, we do not have to be frustrated when we think. In contrast, if we have no systematic method, Problem Solving frustrate us. This reports lists five systematic thinking processes such as rational thinking, systems thinking, cause & effect thinking, contingent thinking, and the Toyotafs five times WHYs method .
Rational thinking
Rational thinking is one of the most common Problem Solving methods. This report will briefly show this Problem Solving method.
Set the ideal situation
Identify a current situation
Compare the ideal situation and the current situation, and identify the problem situation
Break down the problem to its causes
Conceive the solution alternatives to the causes
Evaluate and choose the reasonable solution alternatives
Implement the solutions
We can use rational thinking as a Problem Solving method for almost all problems.
Systems thinking
Systems thinking is a more scientific Problem Solving approach than the rational thinking approach. We set the system, which causes problems and analyze them based on systemsf functions. The following arre the system and how the system works.
System
Purpose
Input
Output
Function
Inside cause (Solvable cause)
Outside cause (Unsolvable cause)
Result
In order to realize Purpose, we prepare Input and through Function we can get Output. But Output does not necessarily realize Purpose. Result of the Function may be different from Purpose. This difference is created by Outside Cause and Inside Cause. We can not solve Outside Cause but we can solve Inside Cause. For example, when we want to play golf, Purpose is to play golf. If we can not play golf, this situation is Output. If we can not play golf because of a bad weather, the bad weather is Outside Cause, because we can not change the weather. In contrast, if we cannot play golf because we left golf bags in our home, this cause is solvable. Then, that we left bags in our home is an Inside Cause.
Systems thinking is a very clear and useful method to solve problems.
Cause & effect thinking
Traditionally, we like to clarify cause and effect relations. We usually think of finding causes as solving problems. Finding a cause and effect relation is a conventional basic Problem Solving method.
Contingent thinking
Game Theory is a typical contingent thinking method. If we think about as many situations as possible, which may happen, and prepare solutions for each situation, this process is a contingent thinking approach.
Toyotafs five times WHYs
At Toyota, employees are taught to think WHY consecutively five times. This is an adaptation of cause and effect thinking. If employees think WHY and find a cause, they try to ask themselves WHY again. They continue five times. Through these five WHYS, they can break down causes into a very specific level. This five times WHYs approach is very useful to solve problems.
Thinking patterns for efficient thinking
In order to think efficiently, there are several useful thinking patterns. This report lists five patterns for efficient thinking such as hypothesis thinking, conception thinking, structure thinking, convergence & divergence thinking, and time order thinking.
Hypothesis thinking
If we can collect all information quickly and easily, you can solve problems very efficiently. But actually, we can not collect every information. If we try to collect all information, we need so long time. Hypothesis thinking does not require collecting all information. We develop a hypothesis based on available information. After we developed a hypothesis, we collect minimum information to prove the hypothesis. If the first hypothesis is right, you do not have to collect any more information. If the first hypothesis is wrong, we will develop the next hypothesis based on available information. Hypothesis thinking is a very efficient problem-solving method, because we do not have to waste time to collect unnecessary information.
Conception thinking
Problem Solving is not necessarily logical or rational. Creativity and flexibility are other important aspects for Problem Solving. We can not recognize these aspects clearly. This report shows only what kinds of tips are useful for creative and flexible conception. Following are portions of tips.
To be visual.
To write down what we think.
Use cards to draw, write and arrange ideas in many ways.
Change positions, forms, and viewpoints, physically and mentally.
We can imagine without words and logic, but in order to communicate to others, we must explain by words and logic. Therefore after we create ideas, we must explain them literally. Creative conception must be translated into reasonable explanations. Without explanations, conception does not make sense.
Structure thinking
If we make a structure like a tree to grasp a complex situation, we can understand very clearly.
Upper level should be more abstract and lower level should be more concrete. Dividing abstract situations from concrete situations is helpful to clarify the complex situations. Very frequently, problem solvers cannot arrange a situation clearly. A clear recognition of a complex situation increases efficiency of Problem Solving.
Convergence & divergence thinking
When we should be creative we do not have to consider convergence of ideas. In contrast, when we should summarize ideas we must focus on convergence. If we do convergence and divergence simultaneously, Problem Solving becomes inefficient.
Time order thinking
Thinking based on a time order is very convenient, when we are confused with Problem Solving. We can think based on a time order from the past to the future and make a complex situation clear.
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What is reading comprehension and how does it relate to college learning?

Excerpt from Arieta, C., "College Active Reading Skills," Promoting Academic Success for Students with Learning Disabilities: The Landmark College Guide. Ed. Strothman, S.W.


Notions of reading comprehension have changed dramatically over the decades. Theories of learning have shifted dramatically during the 20th century. We have moved from a behavioral perspective, which dominated the field from the turn of the century to the sixties and seventies, to a holistic or interactive approach, which began in the late seventies, and continues to shape our thinking about reading comprehension today. Practitioners of the interactive model view reading as a cognitive, developmental, and socially constructed task that goes beyond understanding the words on a page. In the past, reading was considered a relatively static activity. Meaning was imbedded in the text, and the reader's job was to understand what was being transmitted via the words on the page. Current research views reading as a more dynamic process in which the reader "constructs" meaning based on information he/she gathers from the text. Reading expert Katherine Maria (1990) defines reading comprehension as:


...holistic process of constructing meaning from written text through the interaction of (1) the knowledge the reader brings to the text, i.e., word recognition ability, world knowledge, and knowledge of linguistic conventions;(2) the reader's interpretation of the language that the writer used in constructing the text; and (3) the situation in which the text is read. (p. 14-15)


College-level reading is much more sophisticated than high school, and in a typical course load, students may encounter a plethora of literary genres that they are required to read, understand, and apply in a meaningful way. Comprehending these texts is crucial for academic success, yet in an average class, there will be little or no attention paid to the reading process or the strategy training that is so important to the learning tasks.


The role of metacognition in the reading process

Metacognition is vital to academic success. When applied to reading tasks, metacognition involves several elements: the ability to recognize errors or contradictions in text, the understanding of different strategies to use with different kinds of text, and the ability to distinguish important ideas from unimportant ones (Nist and Mealey, 1991). While research suggests that many college students lack metacognitive skills (Baker, 1985), intervention studies also indicate that college students can learn to monitor their level of text comprehension by employing a variety of strategies. Studies also show that college-age students are more motivated to use strategies than younger, less experienced students. "Older students seem better able to regulate and control their understanding than do younger children... as children become older, their capacity to use metacognitive skills increases, and their reasons for not using these skills change" (Nist and Mealey, 1991). There are many reading strategies that can help students improve both comprehension and metacognition. This chapter will help faculty to better understand the complex nature of reading as a process, and also to develop comprehension strategies for students (McNeil, 1992).


Schema theory and reading comprehension

Schema theory, now widely accepted as playing a key role in reading comprehension, is based on the assumption that the reader's prior knowledge directly impacts new learning situations. While schema theory has existed in various forms since the 1930's, it has recently re-emerged and has been redefined as an important concept in reading instruction. Reading theorists view schema theory as a "framework" that organizes knowledge in memory by putting information into the correct "slots," each of which contains related parts. When new information enters memory, it not only must be compatible with one of the slots, but it must actually be entered into the proper slot before comprehension can occur (Nist & Mealey, 1991). If we accept this notion, reading shifts from a text-based activity to an interactive process in which the reader constructs meaning by interacting with the text. According to reading specialist John McNeil (1992), schemata are the reader's "concepts, beliefs, expectations, processes — virtually everything from past experiences that are used in making sense of reading. In reading, schemata are used to make sense of text; the printed word evokes the reader's experiences, as well as past and potential relationships" (p. 20).


Reading teachers emphasize three types of schemata:(1) knowledge of the concepts and processes that pertain to certain subject matter, i.e., science, math, humanities;(2) general world knowledge i.e., social relationships, causes and effects;(3) knowledge of rhetorical structures i.e., patterns, rules, structures for organizing text and cues to the reader. The strategies contained in this chapter are rooted in the principles of schema theory and metacognition and view reading as a dynamic process.


While this handbook is intended for college faculty and staff, the goal is for students to develop an awareness of their own reading process and apply effective reading strategies to address the wide range of reading tasks they will encounter.


Understanding the Reader's Role in theUnderstanding Comprehension Process

Since reading is an interactive process that is dynamic and constantly changing, each new task or assignment will alter the learning process, and challenge the reader to be active in her approach to the text. Developing readers are often challenged with the changing nature of reading tasks. They may also lack some of the strategies that expert readers employ as they read. Because of this, students should be encouraged to take an active role in their learning process. Likewise, instructors play an important role in preparing students for the task and can help students become more aware of the reading characteristics they bring to the task.


Have students respond to a personal reading questionnaire at the onset of a reading assignmentOne way of fostering students' understanding of their reading strategies is to have them complete a reading questionnaire (see below) before they begin the reading assignment. This exercise builds metacognition and plants the seeds for strategy selection. An activity of this nature could be completed in class, and students could share their plan with a partner or utilize for individual reflection.


Questions for Pre-Reading Reflection

1. What type of reading is this? (Textbook, article/essay, or short story.)
2. Is this type of reading a strength or area of difficulty for you?
3. How long is the reading and how much time do you have to complete it?
4. What is your interest in this reading? How can you relate it to your life?
5. What do you already know about the topic?
6. What are some things you might need to read outside of class to gain more background knowledge?
7. If decoding is a problem for you, are there services on campus, such as a learning center or tutor that might be of help to you?
8. What is the purpose of the reading assignment?
9. My personal reading plan for completing this assignment:


Familiarize yourself with the characteristics of students with learning disabilities and dyslexia

When students with learning disabilities or dyslexia struggle with decoding, they will often have to sound out syllables and words, and tend to read word-for-word rather than in phrases or chunks. Reading word-for-word creates numerous one-word chunks, far too many to be held in working memory and called up later for processing meaning. Furthermore, readers who are consumed by these phonological aspects of the text are unable to devote time to processing at the sentence and paragraph level. When most of their effort goes into decoding the words on the page, there is little energy left over for constructing meaning. Obviously, this type of processing will directly impact comprehension.


Have students read aloud in class to gain a sense of their decoding ability

Reading aloud in class can be a valuable diagnostic tool, and can be built into class activities when new readings are introduced. Since students with a history of reading difficulties might be reluctant to read aloud in class, it is important to create an environment of safety, trust, and respect for all. Have students take turns reading short excerpts from the text and allow students to pass if they indicate discomfort with this activity. These students may opt to read aloud with you privately after class. When reading aloud becomes a familiar part of the class, students will become more comfortable with it, and more willing to participate. Reading aloud (especially using an overhead in addition to texts) also gives an opportunity to model active reading strategies (highlighting significant information, chunking, or making brief summary notes or response symbols in the margin).


• Refer students to appropriate support services and provide copies of course readings to support staff who will assist students with your coursework;
• Allow and encourage the use of assistive technology in completing readings for your course.
There are a number of effective reading software programs that are reasonably priced and easy to install. One that stands out for versatility is the Kurzweil™ assistive reading software. Text can be scanned and the computer reads aloud to the student. Students can interact with the text in a number of ways. Here are some suggestions for helping students to use Kurzweil™ for active learning:
• Use Kurzweil™ for a "read-aloud," but encourage students to follow along with a hard copy and mark the text appropriately with margin notations, questions, and vocabulary notation.
• Use Kurzweil™ for notetaking. It is possible to take two-column notes with this software, extracting main ideas and details. This is another way for students to stay active.
• Use Kurzweil™ for vocabulary development. Unfamiliar words and terms can be noted and the Kurzweil™ can be used as a dictionary. Note: it is important to teach students explicitly to use a dictionary effectively.

Comprehension: Theories

INTRODUCTION
The main purpose for reading is to comprehend the ideas in the material. Without comprehension, reading would be empty and meaningless. In our practicum, we have all witnessed cases where students are capable of reading the words, but face much difficulty in expressing their comprehension of the main ideas. An example of this occurrence was a second grade boy named Reggie who loved to read but had difficulty in comprehending what he read. Reggie would eagerly read to an audience since he had a solid grasp of phonemic awareness (sounding out words) and social discourse (reading with expression). When tested by the Reading Specialist, Reggie was placed in a relatively low level reading group. This was due to his inability to demonstrate comprehension of the reading material. This was shocking to the teacher, as he appeared to be a strong reader.
As educators, we need to have an understanding of the theories behind reading comprehension, as well as a working knowledge of some important strategies that can be used in the classroom to increase reading comprehension. In this paper, we are going to focus on three important theories on reading comprehension: the Schema Theory; Mental Models, and the Propositional Theory, and four categories of strategies to improve reading comprehension based on these theories: Preparational, Organizational, Elaboration, and Monitoring.
REVIEW OF LITERATURE
THEORY
Gunning (1996) identifies three main theories of reading comprehension. These theories are Schema Theory, Mental Models, and Proposition Theory.
Schema Theory
Gunning (1996) defines a schema as the organized knowledge that one already has about people, places, things, and events. Kitao (1990) says the schema theory involves an interaction between the reader’s own knowledge and the text, which results in comprehension. This schema, as Gunning defined, can be very broad, such a schema for natural disasters, or more narrow, such as a schema for a hurricane. Each schema is "filed" in an individual compartment and stored there. In attempting to comprehend reading materials, students can relate this new information to the existing information they have compartmentalized in their minds, adding it to these "files" for future use. Based on the Schema Theory, depending on how extensive their "files" become, their degree of reading comprehension may vary.
Mental Model Theory
Another major theory we would like to discuss is the Mental Model. This model can be thought of as a mind movie created in one's head, based on the reading content. Gunning gives a detailed description of this process, stating that a mental model is constructed most often when a student is reading fiction. The reader focuses in on the main character and creates a mental model of the circumstances in which the character finds him or herself. The mental model is re-constructed or updated to reflect the new circumstances as the situation changes, but the items important to the main character are kept in the foreground according to Gunning, (1996).
Perkins (1991) identifies that sometimes misconceptions about important concepts reflect misleading mental models of the topic itself or the subject matter within which it sits. There are, however, interventions the teacher can do to help the reader to stay on track and create a more accurate picture. One suggestion is for the teachers to ask the students to disclose their mental models of the topics in question, through analogy, discussion, picturing, and other ways. This information gives the teacher insight on the student's knowledge gaps and misconceptions, therefore allowing them to help students reconstruct a more accurate picture.
Proposition Theory
The final explanation of comprehension we would like to discuss is the Propositional Theory. This involves the reader constructing a main idea or macrostructure as they process the text. These main ideas are organized in a hierarchical fashion with the most important things given the highest priority to be memorized (Gunning, 1996).

Reading comprehension

Reading comprehension is defined as the level of understanding of a writing. For normal reading rates (around 200-220 words per minute) an acceptable level of comprehension is above 75%.[citation needed]
Proficient reading depends on the ability to recognize words quickly and effortlessly. [1] If word recognition is difficult, students use too much of their processing capacity to read individual words, which interferes with their ability to comprehend what is read.
Many educators in the USA believe that children need to learn to analyze text (comprehend it) even before they can read it on their own, and comprehension instruction generally begins in pre-Kindergarten or Kindergarten. But other US educators consider this reading approach to be completely backward for very young children, arguing that the children must learn how to decode the words in a story through phonics before they can analyze the story itself.
During the last century comprehension lessons usually comprised students answering teachers' questions, writing responses to questions on their own, or both. The whole group version of this practice also often included "round robin reading," wherein teachers called on individual students to read a portion of the text (and sometimes following a set order). In the last quarter of the 20th century, evidence accumulated that the read-test methods assessed comprehension more than they taught it. The associated practice of "round robin" reading has also been questioned and eliminated by many educators.
Instead of using the prior read-test method, research studies have concluded that there are much more effective ways to teach comprehension. Much work has been done in the area of teaching novice readers a bank of "reading strategies," or tools to interpret and analyze text.[2] There is not a definitive set of strategies, but common ones include summarizing what you have read, monitoring your reading to make sure it is still making sense, and analyzing the structure of the text (e.g., the use of headings in science text). Some programs teach students how to self monitor whether they are understanding and provide students with tools for fixing comprehension problems.
Instruction in comprehension strategy use often involves the gradual release of responsibility, wherein teachers initially explain and model strategies. Over time, they give students more and more responsibility for using the strategies until they can use them independently. This technique is generally associated with the idea of self-regulation and reflects social cognitive theory, originally conceptualized by Albert Bandura.[