the assumption that there is a single established body of mathematical skills that everyone needs to know to be prepared for 21st-century careers. This assumption is wrong. The truth is that different sets of math skills are useful for different careers, and our math education should be changed to reflect this fact.
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How to Fix Our Math Education - NYTimes.com - 63 views
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Today, American high schools offer a sequence of algebra, geometry, more algebra, pre-calculus and calculus (or a “reform” version in which these topics are interwoven). This has been codified by the Common Core State Standards, recently adopted by more than 40 states. This highly abstract curriculum is simply not the best way to prepare a vast majority of high school students for life.
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A math curriculum that focused on real-life problems would still expose students to the abstract tools of mathematics, especially the manipulation of unknown quantities. But there is a world of difference between teaching “pure” math, with no context, and teaching relevant problems that will lead students to appreciate how a mathematical formula models and clarifies real-world situations.
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For instance, how often do most adults encounter a situation in which they need to solve a quadratic equation? Do they need to know what constitutes a “group of transformations” or a “complex number”? Of course professional mathematicians, physicists and engineers need to know all this, but most citizens would be better served by studying how mortgages are priced, how computers are programmed and how the statistical results of a medical trial are to be understood.
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Imagine replacing the sequence of algebra, geometry and calculus with a sequence of finance, data and basic engineering.
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Traditionalists will object that the standard curriculum teaches valuable abstract reasoning, even if the specific skills acquired are not immediately useful in later life. A generation ago, traditionalists were also arguing that studying Latin, though it had no practical application, helped students develop unique linguistic skills. We believe that studying applied math, like learning living languages, provides both useable knowledge and abstract skills.
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In math, what we need is “quantitative literacy,” the ability to make quantitative connections whenever life requires (as when we are confronted with conflicting medical test results but need to decide whether to undergo a further procedure) and “mathematical modeling,” the ability to move practically between everyday problems and mathematical formulations (as when we decide whether it is better to buy or lease a new car).
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Education Theory/Constructivism and Social Constructivism - UCD - CTAG - 56 views
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Deep roots classical antiquity. Socrates, in dialogue with his followers, asked directed questions that led his students to realize for themselves the weaknesses in their thinking.
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Emphasis is on the collaborative nature of learning and the importance of cultural and social context.
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Believed that constructivists such as Piaget had overlooked the essentially social nature of language and consequently failed to understand that learning is a collaborative process.
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Constructivist learning environments emphasize authentic tasks in a meaningful context rather than abstract instruction out of context.
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Constructivist learning environments provide learning environments such as real-world settings or case-based learnin
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Constructivist learning environments support "collaborative construction of knowledge through social negotiation, not competition among learners for recognition.
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There is no absolute knowledge, just our interpretation of it. The acquisition of knowledge therefore requires the individual to consider the information and - based on their past experiences, personal views, and cultural background - construct an interpretation of the information that is being presented to them.
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Teaching styles based on this approach therefore mark a conscious effort to move from these ‘traditional, objectivist models didactic, memory-oriented transmission models’ (Cannella & Reiff, 1994) to a more student-centred approach.
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Students ‘construct’ their own meaning by building on their previous knowledge and experience. New ideas and experiences are matched against existing knowledge, and the learner constructs new or adapted rules to make sense of the world
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John Dewey rejected the notion that schools should focus on repetitive, rote memorization & proposed a method of "directed living" – students would engage in real-world, practical workshops in which they would demonstrate their knowledge through creativity and collaboration
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Piaget rejected the idea that learning was the passive assimilation of given knowledge. Instead, he proposed that learning is a dynamic process comprising successive stages of adaption to reality during which learners actively construct knowledge by creating and testing their own theories of the world.
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A common misunderstanding regarding constructivism is that instructors should never tell students anything directly but, instead, should always allow them to construct knowledge for themselves. This is actually confusing a theory of pedagogy (teaching) with a theory of knowing. Constructivism assumes that all knowledge is constructed from the learner’s previous knowledge, regardless of how one is taught. Thus, even listening to a lecture involves active attempts to construct new knowledge.
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Bruner builds on the Socratic tradition of learning through dialogue, encouraging the learner to come to enlighten themselves through reflection
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Careful curriculum design is essential so that one area builds upon the other. Learning must therefore be a process of discovery where learners build their own knowledge, with the active dialogue of teachers, building on their existing knowledge.
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Social constructivism was developed by Vygotsky. He rejected the assumption made by Piaget that it was possible to separate learning from its social context.
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By the 1980s the research of Dewey and Vygotsky had blended with Piaget's work in developmental psychology into the broad approach of constructivism
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1. Discovery Learning (Bruner) In discovery learning, the student is placed in problem solving situations where they are required to draw on past experiences and existing knowledge to discover facts, relationships, and new information. Students are more likely to retain knowledge attained by engaging real-world and contextualised problem-solving than by traditional transmission methods. Models that are based upon discovery learning model include: guided discovery, problem-based learning, simulation-based learning, case-based learning, and incidental learning.
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Teaching Metacognition - 78 views
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Step 1: Teach students that the ability to learn is not a fixed quantity The key to a student's ability to become a self-regulated (i.e., metacognitive) learner is understanding that one's ability to learn is a skill that develops over time rather than a fixed trait, inherited at birth.
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Step 3: Give students opportunities to practice self-monitoring and adapting Accurate self-monitoring is quite difficult.
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In particular, students are encouraged to think about the key points of the lecture as they listen and take notes. At the end of the lecture, students write what they think the three most important ideas of the lecture were on an index card.
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Teaching Self-Monitoring Strategies Monitoring and adapting strategies can be taught as learning habits. A wrapper is one tool for teaching self-monitoring behavior. A wrapper is an activity that surrounds an existing assignment or activity and encourages metacognition. For example, wrappers can be used with lectures, homework assignments, or exams. Wrappers require just a few extra minutes of time, but can have a big impact.
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Example: homework wrappers Before beginning a homework assignment, students answer a brief set of self-assessment questions focusing on skills they should be monitoring. Students complete the homework as usual, and then answer a follow-up set of self-assessment questions.
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Example: exam wrappers When graded exams are returned (as soon as possible after the exam was given), students complete an exam reflection sheet. They describe their study strategies, analyze the mistakes they made, and plan their study strategies for the next exam.
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"Metacognition is a critically important, yet often overlooked component of learning. Effective learning involves planning and goal-setting, monitoring one's progress, and adapting as needed. All of these activities are metacognitive in nature. By teaching students these skills - all of which can be learned - we can improve student learning. There are three critical steps to teaching metacognition:"
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Really useful reminder of how we need to address very basic ideas about how to absorb new information and ask students to self-monitor and push themselves. I appreciated the information and plan to incorporate the wrappers!
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Educational Leadership:Reading: The Core Skill:The Challenge of Challenging Text - 131 views
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The new standards instead propose that teachers move students purposefully through increasingly complex text to build skill and stamina.
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Students' ability to comprehend a piece of text depends on the number of unfamiliar domain-specific words and new general academic terms they encounter.
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If students are to interpret the meanings such complex sentence structures convey, they need to learn how to make sense of the conventions of text—phrasing, word order, punctuation, and language.
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Students who are aware of the patterns authors use to communicate complex information have an advantage in making sense of text.
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Students' background knowledge, including developmental, experiential, and cognitive factors, influences their ability to understand the explicit and inferential qualities of a text.
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even students who have basic decoding skills sometimes struggle to deploy these skills easily and accurately enough to get a purchase on challenging text. To help these students develop reading fluency, teachers should give them lots of practice with reading the same text, as well as instruction to help them develop a stronger sense of where to pause in sentences, how to group words, and how their voices should rise or fall at various junctures when reading aloud.
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pair repeated readings of the same text with questions that require the student to read closely for detail and key ideas.
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In contrast, in reading history and literature, readers need to be concerned with not just the causes of events, but also the human intentions behind these causes.
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teachers should not convey so much information that it spoils the reading or enables students to participate in class without completing the reading; rather, they should let students know what learning to expect from the reading.
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Teachers may be tempted to try to make it easier for students by avoiding difficult texts. The problem is, easier work is less likely to make readers stronger.
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Students experience success in the company of their teacher, who combines complex texts with effective instruction.
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Statistics - Introduction to Basic Concepts - 66 views
bobhall.tamu.edu/...Introduction.html
Topic 2 measures of center real world IADA spread graphic representation
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Erikson's Stages of Development at Learning Theories - 24 views
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Erikson’s Stages of Development Erik Erikson, a German psychoanalyst heavily influenced by Sigmund Freud, explored three aspects of identity: the ego identity (self), personal identity (the personal idiosyncrasies that distinguish a person from another, social/cultural identity (the collection of social roles a person might play). Erikson’s psychosocial theory of development considers the impact of external factors, parents and society on personality development from childhood to adulthood. According to Erikson’s theory, every person must pass through a series of eight interrelated stages over the entire life cycle. Infant (Hope) – Basic Trust vs. Mistrust Toddler (Will) – Autonomy vs. Shame Preschooler (Purpose) – Initiative vs. Guilt School-Age Child (Competence) – Industry vs. Inferiority Adolescent (Fidelity) – Identity vs. Identity Diffusion Young Adult (Love) – Intimacy vs. Isolation Middle-aged Adult (Care) – Generativity vs. Self-absorption Older Adult (Wisdom) – Integrity vs. Despair
Jan's Illustrated Computer Literacy 101: Computer Basics - 85 views
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Teaching for America - NYTimes.com - 24 views
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75 percent of young Americans, between the ages of 17 to 24, are unable to enlist in the military today because they have failed to graduate from high school, have a criminal record, or are physically unfit.
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Tony Wagner, the Harvard-based education expert and author of “The Global Achievement Gap,” explains it this way. There are three basic skills that students need if they want to thrive in a knowledge economy: the ability to do critical thinking and problem-solving; the ability to communicate effectively; and the ability to collaborate.
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Wagner thinks we should create a West Point for teachers: “We need a new National Education Academy, modeled after our military academies, to raise the status of the profession and to support the R.& D. that is essential for reinventing teaching, learning and assessment in the 21st century.”
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All good ideas, but if we want better teachers we also need better parents — parents who turn off the TV and video games, make sure homework is completed, encourage reading and elevate learning as the most important life skill.
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Diigo Groups is Future of Social Bookmarking | Get A New Browser - 0 views
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I’ve been loving Diigo since I ditched Delicious a few months ago. They are constantly adding awesome features and today I stumbled on the groups feature. Basically it allows you to create a group of like-minded users (it can be public or private) to share links, comments and it has a forum baked right in.
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This is HUGE… It allows you to create micro communities and adds much greater value to “social” bookmarking. You can be a part of multiple groups - which are often topical in nature. There are all kinds of different options that allow you to discuss bookmarks in comment threads and in a forum. There are RSS feeds for each group - so you don’t even have to join one to get some benefit. And there’s a great “slideshow” feature that will allow you to quickly lopp through the bookmarked sites.
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Dawn of the cyberstudent | University challenge | guardian.co.uk - 0 views
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students often have more experience of using new technologies than many university managers — even if they need guidance in using them effectively
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the research process is likely to become much more open
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a balance that suits them, which may lead to more varying degrees of face-to-face and online contact,
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"If you are in Second Life listening to a lecture, your ability to fly through a bush isn't that relevant,
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All this will put added pressure on university staff, with increasing demands to respond to students 24/7. Read suggests one answer could be for universities in different parts of the world to share the load so that, as often happens already in industry "the work moves around with the sun".
Basic Paragraph Structure - 0 views
Basic Guide to Essay Writing - 1 views
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Clive Thompson on the New Literacy - 3 views
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The fact that students today almost always write for an audience (something virtually no one in my generation did) gives them a different sense of what constitutes good writing. In interviews, they defined good prose as something that had an effect on the world. For them, writing is about persuading and organizing and debating, even if it's over something as quotidian as what movie to go see. The Stanford students were almost always less enthusiastic about their in-class writing because it had no audience but the professor: It didn't serve any purpose other than to get them a grade.
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The brevity of texting and status updating teaches young people to deploy haiku-like concision.
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When Lunsford examined the work of first-year students, she didn't find a single example of texting speak in an academic paper.
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Stanford 1st year students - check the applicant profile - http://www.stanford.edu/dept/uga/basics/selection/profile.html These are among the top tiered students in the country.
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know is that knowing who you're writing for and why you're writing might be the most crucial factor of all.
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(something virtually no one in my generation did) gives them a different sense of what constitutes good
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"I think we're in the midst of a literacy revolution the likes of which we haven't seen since Greek civilization," she says. For Lunsford, technology isn't killing our ability to write. It's reviving it—and pushing our literacy in bold new directions
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Before the Internet came along, most Americans never wrote anything, ever, that wasn't a school assignment
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Lunsford's team found that the students were remarkably adept at what rhetoricians call kairos—assessing their audience and adapting their tone and technique to best get their point across.
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(something virtually no one in my generation did) gives them a different sense of what constitutes good
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Education World ® : Curriculum: You've Got E-Mail -- But Can You Make It Real... - 1 views
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"Before you begin a telecollaborative project," she said, "Look at the plan critically and decide whether it's worth it in terms of learning outcomes. Ask yourself these questions: Does this use of the Internet allow students to do something that can't be done in another way? Does this use of the Internet allow students to do something in a better way? "If the answer to either of those questions is yes," said Harris, "then your project is probably worth doing." "As teachers, we need to do what is our art and our craft -- which is teaching, not technology."
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An activity structure, according to Harris, is simply a description of what students do in an activity, without reference to content or grade level. For example, kindergarten students mixing paints, elementary students forming compound words, and high-school students creating chemical compounds are all using an activity structure that involves combining existing elements to form new elements. The content and grade level are strikingly different, but the basic activity, the structure of the activity, is the same. Existing activity structures, said Harris, are usually supported best by existing instructional tools. If Internet tools are going to be used to enable students to do something they haven't been able to do, or do as well, before, new activity structures, structures that are best supported by new instructional tools, must be identified and implemented.
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Establish a clear schedule, set interim deadlines, and send out reminders as deadlines approach
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Be sure students have regular access to computers. Once a week in a computer lab is not enough time. For students to get the most out of a telecomputing project, they must be able to participate at least two or three times a week.