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Test Taking Tips
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Test-taking Strategies Physiological Preparation:
Do not eat any heavy meals No smoking No Alcohol Exercise Eat Natural Carbohydrates Get at least 8 hours of sleep Try to wake up at least 2 hours before the test Don't "hunch" over your test Develop a study plan that works for you Be prepared for the test Be comfortable with the test you are taking Test Taking:
Read all questions very carefully Do not change your first response Understand the type of test you are taking Start with the section that you know the best On reading comprehension questions do not read the paragraph but read the questions first On an essay test write outlines Write in simple sentences on an essay testUse page balancing techniques Do not panic Intellectual Preparation:
Study the test by sections Do not study the minute details Look at information as a body of knowledge Do not study chronological order Review the test content categories Review class notes and textbooks Join a study group Avoid cramming for the exam Review the Test at a Glance Booklets Clues for Multiple Choice Test:
Follow Directions Pace your work Read Carefully Determine the "best" answer Guess wisely Mark your answers carefully Have a strategy for handling reading passages Estimate answers Know how to make abstract situations concrete Check the accuracy of your work Constructed-Response Test Tips
Read Directions carefully Pace your activities Organize your response Write your Response Review your responseWriting Praxis II Essays
The process of writing begins with three stages: Prewriting, Drafting, and Editing/Revising
Stages of Writing
I. Prewriting:
The first stage of the writing process.
Decisions to make about why to write, what to write about, which aspect of the topic to focus on, who the audience will be, and which approach to take.
Make brief notes, organizing your topic ideas and supporting evidence.
II. Writing/Drafting:
The second stage of the writing process.
Ideas take form . . . details are reduced to words, key points to phrases.
Thoughts are forged into sentences and sentences are gathered into paragraphs.
III. Editing and Revising:
Major part of writing an essay.
Proofreading--making sure all words are spelled correctly, all sentences are complete, and the writing is mechanically sound.
Revising focuses on meaning and clarity, interesting word choice, sentence variety and linguistic complexity, etc.
Essay Writing
Read the question carefully, word for word! Answer the question completely! Your response should display a cohesive structure, evidence to support and amplify your general statements, and appropriate use of concepts and terminology. What Do These Essays Ask?
Short answer essays in the Praxis II are based upon the principles of learning by using a case study approach to measure your knowledge of three grade levels: K-6, 5-9, 7-12. Know how to use manipulatives to teach reading and math in order to solve vocabulary, reading and math problems students may have. Know several ways to assess a lesson. Topics Covered:
I. Organizing content knowledge for student learning:
Becoming familiar with relevant aspects of students’ background knowledge and experiences. Articulating clear learning goals for lessons that are appropriate for students. Demonstrating an understanding of the connections between the content that was learned previously, the current content, and the content that remains to be learned in the future. Creating or selecting teaching methods, learning activities, and instructional materials or other resources that are appropriate for the students and are aligned with the goals of the lesson. Creating selecting evaluation strategies that are appropriate for students and are aligned with the goal of the lesson. II. Creating an environment for student learning.
Creating a climate that promotes fairness. Establishing and maintaining rapport with students. Communicating challenging learning expectations to each student. Establishing and maintaining consistent standards of classroom behavior. Making the physical environment as safe and conductive to learning as possible. III. Teaching for student learning.
Making learning goals and instructional procedures clear to students. Making content comprehensible to students. Encouraging students to extend their thinking. Monitoring students’ understanding of content through a variety of means, providing feedback to students to assist learning, and adjusting learning activities as the situation demands. Using instructional time effectively. IV. Teacher Professionalism
Reflecting on the extent to which learning goals were met. Demonstrating a sense of efficacy. Building professional relationships with colleagues to share teaching insights and coordinate learning activities for students. Communicating with parents or guardians about student learning. Scoring:
Papers are scored on the writer’s ability to perform the following:
Development and organization of ideas with supporting evidence or specific examples Understanding of the essay’s intended audience Comprehension of the assigned task Skillful use of language Correctness of mechanics usage Paragraphing Some General Tips:
Read the topic twice—three times if necessary—before writing. Circle key words. This will help you focus on the assigned task.Use a form of "prewriting" before you begin writing your actual essay. Spend about 5 minutes organizing your thoughts before you begin writing. A poorly written essay is often the result of inadequate planning.Don’t let spelling slow down your writing. That is, keep the flow of your writing going; then come back later to correct spelling errors. If possible, leave several minutes at the end to reread and edit, correct your essay. Don’t make extensive changes when you reread; just correct spelling errors and other minor flaws. Don’t use excessively large writing, don’t leave wide margins, and don’t skip any lines. Double-check your time allotment and the amount of space you have in which to write each essay. Strategies in Preparing an Essay
I. Clustering
Use pre-writing clustering as a way of organizing your thoughts before you write. After you choose a topic, write it down in the pre-writing area and draw a circle around that topic. For a few moments, think of all the elements of that topic and connect them to the central topic cluster: You can then number the part of the cluster to give an order to your thoughts. Clustering provides a way to put all of your thoughts down on paper before you write, so you can quickly see the structure of the whole paper. The "Story Formula":
One good way to approach a question that asks you to describe the experience is through the use of the "story formula." It consists of: A. Setting—where the story took place
B. Main Characters—who were the people in the story
C. Plot—the problem or crisis in the story to be overcome
D. Climax—the turning point in the story
E. Resolution—the ending, the results of the experience
Example:
Paragraph 1: introduce the setting and the main characters in the story
Paragraph 2: introduce the plot
Paragraph 3: introduce the climax
Final Paragraph: introduce the resolution
The story formula allows you to describe one experience in detail using clear transitions while keeping a unifying them throughout your essay. Outlining
Another way of "prewriting" is outlining Outlining should look like the following: Point One
Example
Example
Point Two
A. Example
B. Example
Example
Point Three
Example
Example
Describe
Describe
Organizing an outline like the one above will help you write a well-structured, well-planned essay. You can readily see that constructing a good essay from the outline above would be a fairly simple task. However you pre-write, whether cluster, outline, or some other way, the important thing is that you think and plan before you actually begin writing your essay! IV. The "Why" Essay
One good way to approach a question which asks you to explain, analyze, or evaluate is to use a "why" essay format. A "why" essay format is built around a thesis sentence. The thesis sentence begins with your opinion, followed by the word "because" and then a list of the most important reasons why the opinion is valid, reasonable, or well founded. The "why" essay format could look like this in outline form: Paragraph 1: Introduction – thesis statement
Paragraph 2: Reason 1
Paragraph 3: Reason 2
Paragraph 4: Reason 3
Paragraph 5: Conclusion
Each paragraph should contain approximately three to five sentences. The introduction invites the reader to read on. Your reasons (3 are often sufficient) that follow should give examples or evidences to support each reason. Your concluding paragraph summarizes your reasons and restates the thesis statement. Important Terms Used in Essay Questions:
Pay close attention to how the essay question is phrased. Are you asked to compare and contrast? Or simply to describe?
Describe: requires the use of adjectives, adverbs, and descriptive type phrases.
Compare: requires analyzing similarities and differences between two or more items.
Explain: requires reason substantiating an opinion or strengthening an argument answers the question why?
Contrast: requires setting up a comparison between items, usually focusing on their differences.
Discuss: usually allows a more open-ended approach, enabling the writer a broader range of possibilities of approach.
Argue (or a point of view): requires the writer to take only one point of view (either pro or con) and substantiate the position. What matters is whichever position you take, that it be soundly and clearly supported.
Essay Checklist
Address the assignment, be well focused Be well organized with smooth transitions between paragraphs coherent, unified. Be well developed and contain specific examples to support points Be grammatically sound (only minor flaws) correct sentence structure, correct punctuation, use of standard written English Use of language skillfully, variety of sentence types, variety of words Be legible, clear handwriting, neat Major Educational Philosophers
Philosophers are not always a part of the Praxis II. Sometimes the tests may contain several and other times they may not have any at all. Here are a few of the major philosophers that you should know just in case you encounter them on the test.
John Amos Kimonos (Comenius) (1592-1670).
Over time, many educators have referred to the great Moravian educational reformer and theorist John Amos Kimonos as the greatest educationalist who ever lived (Egan, 1992). “Comenius's main ideas have become so much a part of our presuppositions about education that we have nothing left to argue about in the way that people still argue about Plato, Rousseau, and Dewey” (Egan, 1992, p. 56). Kimonos proposed a system of systematic learning and lifelong education for everyone. He saw the life of everyone as a school from cradle to grave. To Kimonos, the secret of long life was to never live in idleness, but to engage in useful work and to learn throughout life. He outlined his ideas of a systematic, lifelong education in the Pampaedia as a life cycle which followed the cycles of the year:
The Prenatal School was like the beginning of year and the month of January.The Infant School was like the months of February and March when nature sends forth tender shoots of growth.The School of Boyhood was like April when the plants were furnished with blossoms.The School of Adolescence was like May when all fruits are beginning to develop.The School of Early Manhood was like June when fruits were ripening and producing an early crop.The School of Full Manhood was like the months of July to November when the harvesting of fruits took place.The School of Old Age was similar to December, bringing everything to fulfillment and completing the year's cycle. Comenius's system of schooling distinguished between formal and informal education. Informal education, according to Kimonos, should occur during the first six years of life and take place within the family, with collective preschool education provided for children at ages 5 and 6. Formal education would begin with schooling at the elementary level for children ages 6 through 12 and continue in
secondary schools to age 18. Higher education would continue to age 24. Then, the “schools of life” would provide an informal yet systematic continuing education. The stress that Kimonos placed on systematic learning before and after formal schooling has helped further an understanding of the importance of both preschool and adult education among modern educators.
The best and probably best known of Comenius's textbooks, Orbis Pictus, exemplifies his textbooks and their proclivity for language teaching. Kimonos believed that a language could only be mastered if a person fully comprehended reality, and that effective language teaching inevitably would contribute to
factual knowledge and real information about nature and the world. What contributed to the popularity of the book more than anything else were the inclusion of pictures. Orbis Pictus was intended for children up to age six but it was advocated and used for all ages. Its intent was to develop the cognitive powers, the powers of reason and communication, and also handicraft skills of children.
Looking at the pedagogy of John Amos Kimonos, we see that much of his pedagogy is still valid today. Kimonos believed:
Teaching must be in accordance with the pupil's stage of development. (Kimonos identified four important stages of learning. In the first, senses play an important role; in the second, imagination and memory; in the third, understanding and knowledge; and in the fourth, judgment.)All learning develops through the senses. This makes induction, visual means, and experiences important for learning and teaching.One should proceed from the specific to the general, from what is easy to the more difficult, from the known to the unknown.Teaching should not cover too many subjects or themes at the same time.Teaching should proceed slowly, steadily, and systematically. Nature makes no leaps and jumps.John Dewey (1859-1952).
A native of Vermont and educated at Johns Hopkins University, John Dewey enjoyed a lengthy career as an educator, psychologist, and philosopher and is perhaps the most celebrated educator America has produced. Dewey taught at Michigan, Chicago, and Columbia University, but it was at the University of Chicago where he initiated his progressive laboratory school, putting into practice his reforms in educational methodology which have influenced countless numbers of teachers, teacher educators, and teacher-preparation programs throughout America and the world. Coming from an idealist background, strongly influenced by pragmatism, and an outstanding exponent of naturalism, Dewey believed in practical problem solving. To Dewey, testing rival hypotheses against experience leads to logical and understandable action. Writing in 1916 in his book Democracy and Education, Dewey describes in detail how an ability to respond creatively to continual changes in the natural order is crucial to provide for individual and community life. Dewey recognized that the results of this process are always open to criticism and revision, so that nothing is ever finally and absolutely true. Dewey is largely responsible for bringing much of the European educational thought (which came to America with the influx of immigration after the Civil War) to fruition in American education. Ideas like “hands-on, pupil participatory, learning-by-doing, and activity-oriented learning” plus methods of teaching that include concepts like “thematic units” and “projects” are all traceable to John Dewey.
Eric Erikson
Psychosocial Theory – development consists of a sequence of stages, each defined by a
unique crisis or challenge.
The eight stages of Psychosocial Development in Erikson’s Theory
Psychosocial Stage Age Challenge
Basic trust versus mistrust
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Birth to 1 year
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To develop a sense that the world is safe, a "good place"
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Autonomy versus shame and doubt
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1 to 3 years
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To realize that one is an independent person who can make decisions
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Initiative versus guilt
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3 – 6 years
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To develop a willingness to try new things and to handle failure
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Industry versus inferiority
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6 years - adolescence
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To learn basic skills and to work with others
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Identity versus identity confusion
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Adolescence
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To develop a lasting, integrated sense of self
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Intimacy versus isolation
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Young adulthood
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To commit to another in a loving relationship
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Generativity versus stagnation
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Middle adulthood
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To contribute to younger people, though child rearing, child-care, or other productive work.
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Integrity versus despair
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Late life
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To view one’s life as satisfactory and worth living
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Arnold Gesell
Maturational Theory – the view that child development reflects a specific and prearranged scheme or plan within the body. Behaviors like speech, play, and reasoning would emerge spontaneously according to a predetermined developmental timetable.
Sigmund Freud
Psychodynamic Theory – development is largely determined by how well people resolve
Conflicts they face at different ages.
Theory of Personality
The id is a reservoir of primitive instincts and drives. Present at birth the id presses for immediate gratification of bodily needs and wants. A hungry baby crying illustrates the id.
The ego is the practical, rational component of personality. The ego begins to emerge during the first year of life, as infants learn that they cannot always have what they want.
The superego, emerges during t he preschool years as children begin to internalize adult standards of right and wrong. The superego is the "moral agent" in the child’s personality.
Account of Psychosexual development
He believed that humans want to experience physical pleasure from birth.
John Locke
An infant’s mind is a blank slate on which experience writes.
John Watson
The first person to apply Lock’s approach to child development. He felt that experience
was all that mattered in determining the course of development.
B.F. Skinner
Operant Conditioning – the consequences of a behavior determine whether a behavior is
repeated in the future.
A reinforcement is a consequence that increases the future likelihood of the
behavior that it follows.
A punishment is a consequence that decreases the future likelihood of the
behavior that it follows.
Imitation or observational learning – children learn a lot by watching those
around them.
Jean Piaget
Cognitive Development – focuses on how children think and how their thinking changes
over time.
Piaget’s Four Stages of Cognitive Development:
Stage
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Approximate Age
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Characteristics
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Sensorimotor
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Birth to 2 years
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Infant’s knowledge of the world is based on senses and motor skills. By the end of the period, infant uses mental representations.
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Preoperational thought
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2 to 6 years
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Child learns how to use symbols such as works and numbers to represent aspects of the world, but relates to the world only through his or her perspective.
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Concrete operational thought
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7 to 11
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Child understands and applies logical operations to experiences, provided they are focused on the here and now.
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Formal operational thought
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Adolescence and beyond
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Adolescent or adult thinks abstractly, speculates on hypothetical situations, and reasons deductively about what may be possible.
|
Assimilation – occurs when new experiences are readily incorporated into existing
schemes.
Accommodation – changing existing knowledge based on new knowledge. When disequilibrium occurs, children reorganize their schemes to return to a state of equilibrium, a process that Piaget called equilibration.
Lev Vygotsky
Focused ways that adults convey to children the beliefs, customs, and skills of their culture.
Zone of proximal development – the difference between what a child can do with
assistance and what he can do alone
scaffolding – refers to a teaching style that matches the amount of assistance to the
learners needs.
Urie Bronfenbrenner
Sees the developing child as embedded in a series of complex and interactive systems.
Divides the environment into four levels
Microsystem – consists of the people and objects in an individuals immediate
environment. (parents, siblings) Children can have more than one.
Mesosystem – Microsystems are connected to create the mesosystem. The
This represents the fact that what happens in one microsystem is likely
to influence others. (If you had a stressful day at work then your
grouchy at home.
Exosystem – Refers to social settings that a person may not experience firsthand but
that still influence development. (A mother may pay more attention to
her child when her work is going well and less attention when she’s
under work-related stress.) extended family
Macrosystem – the subcultures and cultures in which the microsystem, mesosystem, and exosystem are embedded. Attitudes, beliefs, and heritage of the culture.
Benjamin BloomLevels of Thinking Complexity
Working Definitions of Higher Cognitive Levels of Thinking
Evaluation – a higher level question. Formulating subjective judgment as the end product resulting in personal values/opinions with no real right or wrong answers
Synthesis – higher order questions that asks the student to perform original and creative thinking.
Analysis – higher order questions that require students to think critically and in depth
Application - Using previously learned information in a new situation to solve problems that have single or best answers (math problems)
Comprehension - Understanding the information and can arrange it mentally
Knowledge – recognize or recall the information
Multiple Intelligences - Howard GardnerMULTIPLE INTELLIGENCES theory, in a nutshell, is a pluralized way of understanding the intellect. Recent advances in cognitive science, developmental psychology and neuroscience suggest that each person's level of intelligence, as it has been traditionally considered, is actually made up of autonomous faculties that can work individually or in concert with other faculties. Howard Gardner originally identified seven such faculties, which he labeled as "intelligences"; recently added an eighth:
Musical Intelligence – our ability to perform and comprehend musically appears to work independently from other forms of intelligence.
Bodily-Kinesthetic Intelligence - each person possesses a certain control of his or her movements, balance, agility and grace
Logical-Mathematical Intelligence - our ability to mentally process logical problems and equations, the type most often found on multiple choice standardized tests
Linguistic Intelligence – the connection between language and the brain
Spatial Intelligence – how we comprehend shapes and images in three dimensions
Interpersonal Intelligence - the ability to interact with others, understand them, and interpret their behavior.
Intrapersonal Intelligence - a person's ability to identify and classify patterns in nature
Naturalist Intelligence - Observing the natural environment and existing relationships
Edward Zigler
Started the Head Start program for pre-school age children
Lawrence Kohlberg: Levels and Stages of Moral Development
Level I: Preconventional Morality (age 4 - 10)
Moral value resides in a person's own needs and wants.
Stage 1: Obedience and Punishment OrientationIndividuals moral judgement is motivated by a need to avoid punishment.Stage 2: Instrumental-Relativist OrientationIndividuals moral judgement is motivated by a need to satisfy own desires. Level II: Conventional Morality (age 10 - 13)
Moral values reside in performing good or right roles, in maintaining the convention order, and in pleasing others
Stage 3:"Good Boy/Nice Girl" OrientationIndividuals moral judgement is motivated by a need to avoid rejection, disaffection, or disapproval from others.Stage 4: Law and Order OrientationIndividuals moral judgement is motivated by a need to not to be criticized by a true authority figure. Level III: Postconventional Morality (adolescence - adulthood)
Moral values reside in principles, separate from those who hold Moral values reside in principles, separate and enforce them, and a part from a person's identification with the enforcing group. Most people never reach this last level.
Stage 5: Legalistic OrientationIndividuals moral judgement is motivated by community respect for all, respecting social order, and living under legally determined laws.Stage 6: Universal, Ethical Orientation.Individuals moral judgement is motivated by ones own conscience. Important Definitions:Reading:
Emergent Literacy – developing awareness of the interrelatedness of oral and written language.Dolch sight word list – 220 of the most common words in reading materialsVisual discrimination – the ability to see likeness and differences among printed words.Context clues – the words phases and sentences surrounding the words to be decoded help readers determine what the unfamiliar words are. Auditory perception – detection of likeness and differences in speech soundsDevelopmentally appropriate practice – a framework or an approach for working with young children in which the teacher considers each child’s competencies and adjusts instruction accordingly.Phonemic Awareness – an understanding that speech consists of a series of small sound units Alphabetic Principle – the concept that letters represent speech soundsSchemata – the clusters of concepts each person develops through experienceVicarious experiences – second hand experiences (videos, film strips, speakers, etc.)Semantic Maps – used to teach students how words are related to one anotherSemantic Feature Analysis – a technique that can help children understand the uniqueness of a word as well as its relationships to other wordsMetacognition – A person's awareness of what strategies are necessary to perform a task and their ability to use self-regulation strategies.Close procedure - The students are given sentences where random words are left out and they are to fill them in.Vowels – letters a, e, i, o, and u represent vowel sounds, and the letters w and y take on the characteristics of vowels when they appear in the final position in a word or syllable. The letter y also has the characteristics of a vowel in the middle position in a word or syllable.Consonants – letters other than the five main vowels. W and Y have the characteristics of consonants when they appear in the initial position in a word or syllable.Consonant Blends (or Clusters) – two or more adjacent consonant letters whose sounds are blended together, with each individual sound retaining its identity. Ex. The sound"str" in the word "strike" can be detected as three sounds.Consonant Digraphs – two adjacent constant letters that represent a single speech sound. Ex. The "sh" in "shore" because it represent one sound.Vowel Digraphs – two adjacent vowel letters that represent a single speech sound. Ex. The "oo" in "foot" is a vowel digraph.Diphthongs – Vowel sounds that are so closely blended that they can be treated as single vowel units for the purposes of word identification. Ex. The "ou" in "out" is a diphthong.Language experience approach - The student writes for the teacher and she uses it as the students reading material.Special Education:adaptive skills - Skills needed to adapt to one's living environment (communication, self-care, home living, social skills, community use, self-direction, health and safety, functional academics, leisure, and work.) and is usually estimated by an adaptive behavior survey.Continuum of alternative placements - The full range of alternative placements, from those assumed to be least restrictive to those considered most restrictive. It ranges from regular classrooms in neighborhood schools to resource rooms, self-contained classes. special day schools, residential schools, hospital schools, and home instruction.mainstreaming - The placement of students with disabilities in general education classes for all or part of the day and for all or only a few classes.least restrictive environment - exceptional children must be educated in as normal an environment as possible.Science:
Scientific Method - 1. Define the problem; 2. Find out what is already known about the problem; 3. Form an hypothesis or educated guess; 4. Conduct an experiment to test the hyposthesis; 5. Use the results to reach a conclusion. Before-The-Test-ChecklistWhat do I need to do before the test?
Know the testing requirements for your teaching field in the state where you plan to teach.Follow all of the test registration procedures.Know the topics that will be covered in each test you plan to take.Review any textbooks, notes and course readings that relate to the topics covered.Know how long the test will take and the number of questions it contains. Consider how you will pace your work.Be familiar with the test directions and the types of questions for your test.Be familiar with the recommended test taking strategies.Practice working through sample tests at a pace similar to that of the actual test.Understand the scoring criteria for the essay section.What do I need to take to the test center?
You must take photo identification with your name and signature to the test center. Acceptable identification includes a photo driver's license, photo employment I.D.,current passport, military identification, or student photo I.D. accompanied by an additional photo or signature I.D. If you registered in your married name and your I.D. is in your maiden name, you must have your marriage license in addition to your photo I.D. If you do not have proper identification, you will not be allowed to take the test and your registration and test fees will not be refunded.You may want to take layered clothing to the test center. The room temperature may vary.You must have your admission ticket, letter of authorization, mailgram or telegram.You may want to take several number 2 pencils, erasers and a blue or black pen for the essay or constructed response portions of the test.You may want to take a watch to keep up with your time.You may want to take a graphing, scientific or four-function calculator for the mathematics portion of the test. Calculators with QWERTY (typewriter) are not allowed. Food, gum, books, papers and tobacco products are not allowed in the testing centers.What do I need to do until then?
Relax!Study!Go to bed early the night before the test.Eat a healthy breakfast on the day of the test.Listen to classical music on your way to the test center.Arrive early and take a walk.Math
Below are the PRAXIS II objectives that will be addressed in the mathematics subject-area assessment.
Arithmetic and Basic Algebra
Solve ratio, proportion, percent, and average (including arithmetic mean and weighted average) problems.Work with algebraic expressions, formulas, and equations.Use the results of the binomial theorem.Present geometric interpretations of algebraic principles.Geometry
NoneTrigonometry
NoneFunctions and Their Graphs
Demonstrate understanding of and ability to work with functions and their graphs including functions given as mapping.Given an equation, graph it; given a graph, determine an equation for it.Determine properties of a functon such as domain, range, intercepts, symmetries, intervals of increase or decrease, discontinuities, and asymptotes.Use the properties of algebraic, trigonometric, logarithmic, and exponential functions to solve problems (for example, finding composite functions and inverse functions).Find the inverse of a one-to-one function in simple cases and know why one-to-one functions have inverses.Probability and Statistics
Organize data into a suitable form (for example, construct a histogram and use it in the calculation of probabilities).Solve discrete and joint probability problems; know when it is appropriate to use independence or probabilities.Solve problems using the binomial distribution and be able to determine when the use of the binomial distribution is appropriate.Know and find the appropriate uses of common measures of central tendency (population mean, sample mean, median, mode) and dispersion (range, population standard deviation, sample standard deviation, population variance, sample variance).Model problems using mathematical expectations of a random variable (for example, fair coins, expected winnings, expected profit).Solve problems using the Normal, Uniform, and Chi-square distributions.Recognize a vail test to determine whether to accept or reject a given Null Hypothesis, H.Analytic Geometry
NoneCalculus
Show that a particular functon is continuous; understand the difference between continuity and differentiability.Use standard differentiation and integraton techniques.Evaluate improper integrals.Discrete Mathematics
Perform elementary operations on sets.Solve basic problems involving permutations and combinations.Linear Algebra
NoneComputer Science
NoneMathematical Reasoning and Modeling
Develop a mathematical model; determine if one model will describe two different situations.Determine appropriate problem solving strategies and consider alternatives. Strategies might include conjectures, counterexamples, inductive reasoning, deductive reasoning (mathematical induction, proof by contradiction, direct proof, and other types of proof) and deciding which tools are appropriate (for example, discussion with others, mental math, pencil and paper, calculator, computer, trees and graphs, fingers, S.W.A.G.).Recognize the reasonableness of results.Estimate answers; determine the accuracy of an estimate by analyzing the effects of roundoff and truncation errors introduced in the course of solving a problem.The Praxis II Math Subject Area Assessment Exam
The exam is two hours long and contains 50 multiple-choice questions, apportioned among topics as shown in the chart below. A page of mathematical notation used is included, as are a few formulas such as the half-angle formulas, DeMoivre's Theorem, and some volume formulas. A few definitions from linear algebra are also included. A graphing calculator is required.
Content Category
|
Group
|
Approximate Number of Questions
|
Arithmetic and Basic Algebra
|
I
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6-8
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Geometry
|
I
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4-6
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Trigonometry
|
I
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2-4
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Analytic Geometry
|
I
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2-4
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Functions and their Graphs
|
II
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5-7
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Calculus
|
II
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5-7
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Probability and Statistics
|
III
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3-5
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Discrete Mathematics
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III
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3-5
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Linear Algebra
|
III
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3-5
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Computer Science
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III
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2-4
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Mathematical Reasoning and Modeling
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III
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5-7
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The numbers of questions are further constrained as follows:
17 questions (34%) from Group I
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12 questions (24%) from Group II
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21 questions (42%) from Group III
|
Praxis II is a test of content knowledge, not of aptitude; therefore, unlike the SAT or GRE, it is possible to do much better on it by studying for it. Also, unlike the GRE, the Praxis II test is not intended to establish your place in a broad spectrum of ability; it is much more a sort of pass/fail test. Because of this the difficulty of the questions on the Praxis II tends to be clustered near the mean (rather than spread out wide as on the GRE).
The information that follows is a summary of all topics found on the test.
Graphing Calculators
You must bring a graphing calculator to the test. Calculator memories will not be cleared. Computers, calculators with QWERTY (typewriter) keyboards, calculators that make noise or plug into an outlet, and electronic writing pads are not allowed--this includes the TI-92. You will be expected to be able to do the following tasks using your graphing calculator:
· produce the graph of a function within an arbitrary viewing window;
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· find the zeros of a function;
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· compute the derivative of a function numerically;
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· compute definite integrals numerically.
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Specific Topics
Each topic that might be on the exam is listed in the following table. Topics labeled "high school" are topics you are expected to know from high school.
Topic
|
Found in
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Arithmetic and Basic Algebra
|
|
(A1) Understand the structure of the natural, integer, rational, real, and complex number systems; have the ability to perform the basic operations (+,-,×,÷) on numbers in these systems; identify properties (e.g., closure, commutativity, associativity, distributivity) of the basic operations
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high school math
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(A2) Given newly defined operations on a number system, determine whether the closure, commutative, associative, or distributive properties hold
|
college
math
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(A3) Demonstrate an understanding of the properties of counting numbers (e.g., prime or composite, even or odd, factors, multiples)
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college
math
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(A4) Solve r |