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.
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.
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 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.
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.
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.
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 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).
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).
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