PDF Archive search engine
Last database update: 25 February at 19:49 - Around 75000 files indexed.
Durch diese Arbeiten werden die Pferde allgemein physisch und psychisch ausgeglichen, lernen die Bewegungsabläufe zu optimieren, alte Schemata können durchbrochen werden.
`A∨⊥≡A (2.4.1) (2.4.4) (2.4.5) (2.4.7) (2.4.10) ` A → B ≡ ¬A ∨ B ` ¬A ∨ B ≡ A ∨ B ≡ B ` A → (B ≡ C) ≡ A → B ≡ A → C ` A ∧ B ≡ ¬(¬A ∨ ¬B) ` A ∨ B ≡ ¬(¬A ∧ ¬B) (2.4.11) (2.4.12) (2.4.13) (2.4.17) (2.4.18) `A∧A≡A `A∧>≡A `A∧⊥≡⊥ (2.4.19) (2.4.20) (2.4.21) 1 Some Theorems of Boolean Logic- continued Distributivity of ∨ over ∧ Distributivity of ∧ over ∨ Distributivity of → over ∧ Ping-Pong Theorem Merge Split Cut Rule Modus Ponens Transitivity of → Proof by Cases ` A ∨ (B ∧ C) ≡ (A ∨ B) ∧ (A ∨ C) ` A ∧ (B ∨ C) ≡ (A ∧ B) ∨ (A ∧ C) (2.4.23(i)) (2.4.23(ii)) ` A → (B ∧ C) ≡ (A → B) ∧ (A → C) ` (A ∨ B) → C ≡ (A → C) ∧ (B → C) ` A ≡ B ≡ (A → B) ∧ (B → A) (2.4.25) (2.4.24) (2.4.26) A, B ` A ∧ B A∨A`A A`A∨B A∧B `A (2.5.1(1)) (2.5.1(2)) (2.5.1(3)) (2.5.1(4)) A ∨ B, ¬A ∨ C ` B ∨ C A ∨ B, ¬A ∨ B ` B A ∨ B, ¬A ` B A, ¬A ` ⊥ (2.5.4) (2.5.5) (2.5.6) (2.5.7) A, A → B ` B A → B, B → C ` A → C (2.5.3) (2.5.9) A → C, B → D ` A ∨ B → C ∨ D A → C, B → C ` A ∨ B → C A → C, ¬A → C ` C (2.5.10) (2.5.11) (2.5.13) 2 Axioms of Predicate Logic The axioms of Predicate Logic consist of all partial generalizations of the following schemata:
The initial conflicting interpretations were maintained and solidified by additional mismatches in discourse management strategies, schemata and contextualization cues.
PRINCIPLES OF LEARNING AND LEARNING THEORY Principles of Learning and Learning Theory Hannah R. Hiles University of North Carolina at Greensboro 1 PRINCIPLES OF LEARNING AND LEARNING THEORY 2 What is learning? > Major Learning Theories: Gagné’s Hierarchy Much of our understanding of education and the teaching process comes from Robert Gagné, an early 20thcentury experimental psychologist who was primarily interested in learning and instruction. It was Gagné who gave us the most fundamental basis for the process of teaching and what the instruction process looks like. Gagné’s Hierarchy of Learning presents eight ways to learn, with each stage building on the lower levels, ensuring that the upper levels require greater skill and ability to conquer. From the bottom up they begin with Signal Learning. As it is at the very bottom of the hierarchy it is part of Pavlov’s “classical conditioning,” or the act of conditioning a subject to provide a desired response in conjunction with a predetermined signal. Next comes StimulusResponse Learning – a more advanced version of classical conditioning. It incorporates the use of schedules and rewards in the learning process. Chaining comes next, wherein a student begins to learn the ability to connect prior lessons together in an organized sequence. After Chaining comes Verbal Association. A higherlevel form of Chaining, Verbal Association is the same idea, but with those prior lessons being vocal in nature as opposed to physical. Note that only halfway up the hierarchy, we are finally at a point where the student is at a point where they are beginning to incorporate verbal skills – the magnitude of Gagné’s hierarchy and just how “basic” his most fundamental lessons are cannot be overstated. Discrimination Learning, Concept Learning, and Rule Learning are next and are very linked together. Discrimination Learning is the process of a student being able to form appropriate responses in an organized and precise way. Concept Learning follows this by PRINCIPLES OF LEARNING AND LEARNING THEORY 3 requiring that the student makes those same responses but now with the addition of categorization – that they respond the same way to the same stimuli, regardless of order or organization. Rule Learning eventually comes in, the second to last piece of Gagné’s hierarchy. The most complex part of Rule Learning is that it requires the student to not only learn relationships between situations and higher concepts but to also predict future situations and concepts (ie, to understand social rules even if they are in a social situation that is new). The final part of Gagné’s Hierarchy is Problem Solving. Gagné considered this the highest level of learning. Because it requires entirely independent cognition and no external stimuli, the student has to have mastered all previous levels in order to problem solve effectively. In Problem Solving, the student must be able to face complicated rules and situations and not know the answers – instead, he or she must know ways of getting to the answers (Singley 1989). Gagné saw that by working their way up through the levels, students could eventually have mastery of the task they were studying. This method also allowed for students to move at a pace that worked for their own abilities, as well as letting them stop and start again at any point and presenting the entire learning process as a journey rather than a means to an end (Clark 2004). > Major Learning Theories: Bloom’s Taxonomy This learning theory comes from a 1956 report that came to be known as “Bloom’s Taxonomy,” a form of learning through instruction that takes into account the intake of information through Cognitive (knowledgebased learning), Affective (emotionbased), and Psychomotor (actionbased). Much of instructional design that takes guidance from Bloom looks specifically at the Cognitive model of Bloom’s Taxonomy, and the six individual components that Bloom organizes in a hierarchy (similar to Gagné’s own hierarchy). For Bloom, the PRINCIPLES OF LEARNING AND LEARNING THEORY 4 hierarchy comes in the form of Remembering, Understanding, Applying, Analyzing, Evaluating, and Creating. It’s important when looking at Bloom’s hierarchy to see that, as with Gagné, each step leads to the next. The student begins with remembering materials – they can recall and repeat facts and answers from their longterm memory with ease. Once they can remember information they can proceed to understand it – one can memorize sums and figures or dates in history without actually understanding what they mean, but Bloom saw this second level of Understanding as an important moment in the educational process. Applying is the student’s use of the information they have come to understand – this will vary depending on the information they have, but the more they use the information at hand, the deeper their understanding of it will come. This leads directly into Analyzing, where a student can look at the work they are doing (their “application” in the previous state of the hierarchy) and determine cause and effect. This work of analyzing their lesson moves organically into Evaluating – if A causes B, and B is a problem, how can the student solve B? This stage of Evaluation is similar to Gagné’s final level of Problem Solving – it is the process of a student looking for the work they are doing and determining where the issues are, then finding for themselves what the solutions may be. Finally, the student can move into Creating. Unlike Gagné, Bloom didn’t see the educational process as stopping at Problem Solving – for him, the pinnacle of mastering a skill or learning something new came when the student was able to then take that information and do something unique with it. Bloom’s first edition of the Taxonomy had this final stage as “Knowledge,” but in 2001 (two years after his death), it was updated to “Creating” or PRINCIPLES OF LEARNING AND LEARNING THEORY 5 “Synthesizing”. This is the student’s ability to take unique and individual parts and put them together into a larger and more unified representation of the lesson or information they have been learning – a synthesis of their learned knowledge (Wineburg 2009). > Major Learning Theories: Behaviorism, Cognitivism, and Constructivism Behaviorism, Cognitivism, and Constructivism are three additional members of learning theory that cannot be neglected. Going back to Gagné’s “signal learning” and Pavlov’s “classical conditioning,” Behaviorism looks at the most simple behavioral changes in an organism. As Jordan et al point out, Behaviorists are quick to defend that they don’t believe learners don’t think, rather “they [researchers] mainly choose to ignore inaccessible mental processes and focus on observable behaviour” (2008). Cognitivism is a step up, branching into the mental processes of how we observe and then process our environments and what happens to us. While Behaviorism may be the kneejerk reactions, Cognitivism in learning relies on “developing effective ways of building schemata and processing information” (Jordan). Finally, in Constructivism, we see yet a further advancement in the realm of cognition. Instead of simply processing information as in Cognitivism, Constructivism is a school which is based on the educator taking a passive role in their pupil’s learning – instead of dishing out answers, they may use questions to inspire their students to probe deeper into their own understanding of the materials, and find their own answers within. Jordan et al note that while the flow between Constructivism and Cognitivism can be difficult to differentiate, Constructivism ultimately “focuses on what people do with information to develop knowledge” (2008).
Und Menschen, die auch nur das kleinste Unbehagen gegen fremde Kulturen und Mentalitäten durchblicken lassen, werden dieser Tage automatisch unter die Schemata von Rechten subsumiert und sind mit einem male Nationalisten, Intolerante, Weltverschlossene bis hin zu Homogenisten und Mörder, obwohl sie nur ihr ehrliches Befinden äußern wollten.