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amacrae

The Third Teacher - 1 views

shared by amacrae on 19 Nov 16 - No Cached
  • 2Getting Started with the Physical EnvironmentOVERALL ...It is both an art and a science to design (as opposed to decorate) a learning environment that responds to our ultimate goal as educators – to develop independent and rigorous thought. Therefore, if we want to foster discovery and reflection, dialogue and the sharing of ideas, the overall physical environment should include:•A large gathering space for whole-group work and discussions, located near whiteboards, easels and/or projector screens.•A gathering space for small-group and whole-group discussions – where students can see clearly the representations of learning that are posted on boards or screens and hear classmates as they share ideas.•Flexible and reconfigurable space for small-group collaborative work and inquiry – space must allow for groupings of various sizes, such as pairs, triads and groups of four or more.•Desks and tables configured to facilitate discussion by allowing eye contact with peers and teacher, the unencumbered flow of traffic and enough space for students to write collaboratively.•Active areas for inquiry, investigation and wonder and quiet areas for thinking and exploring technology – all areas need to be accessible to students for communicating and documenting their own learning (e.g., computers, computer software, tablets, digital cameras and video recorders, document cameras, interactive white boards).•Instructional materials organized in such a way as to provide easy selection and access for all students – materials may include computer software, educational web sites and applications, found materials, graphic organizers, newspapers and other media, resource texts, etc.FOR MATHEMATICS ...Mathematically literate students demonstrate the capacity to “formulate, employ and interpret MATHEMATICS” (OECD, 2012, p. 4); they view themselves as mathematicians, knowing that MATHEMATICS can be used to understand important issues and to solve meaningful problems, not just in school but in life. By extension, the physical environment for MATHEMATICS learning should include: •Spaces where students can use manipulatives to solve problems and record their solutions.•Board and/or wall space to display student solutions for Math Congress and Bansho – student solutions should be easily visible from the group gathering space.•Space to post co-created reference charts such as glossary terms and past and current summaries of learning that specifically support the development of the big ideas currently under study.•Instructional materials organized in such a way as to provide easy selection and access for all students; may include MATHEMATICS manipulatives, calculators and other mathematical tools, mathematical texts, hand-held technology.FOR LITERACY ... Today’s literate learners experience “a constant stream of ideas and information” – they need strategies for interpretation and making sense and lots of practice in identifying meaning, bias and perspective (Ontario Ministry of Education, 2009, 2006). By extension, the physical environment for literacy learning should include: •Spaces where students can talk, listen, read and write.A place for wonder, mystery and discovery ...“We need to think about creating classroom environments that give children the opportunity for wonder, mystery and discovery; an environment that speaks to young children’s inherent curiosity and innate yearning for exploration is a classroom where children are passionate about learning and love school.” (Heard & McDonough, 2009)
  • maintain that the key to learning in today’s world is not just the physical space we provide for students but the social space as well (
  • A large gathering space
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  • mall-
Justin Medved

Mathlete Blogs | Connecting Math Students with Peers From Around the World - 2 views

shared by Justin Medved on 04 Nov 13 - No Cached
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    "MathleteBlogs.com is a resource for mathematics teachers to connect their math students with peers from around the globe to enhance their mathematical learning experience from K-12."
garth nichols

Math Teachers Should Encourage Their Students to Count Using Their Fingers in Class - The Atlantic - 2 views

  • This is not an isolated event—schools across the country regularly ban finger use in classrooms or communicate to students that they are babyish. This is despite a compelling and rather surprising branch of neuroscience that shows the importance of an area of our brain that “sees” fingers, well beyond the time and age that people use their fingers to count.
  • Remarkably, brain researchers know that we “see” a representation of our fingers in our brains, even when we do not use fingers in a calculation
  • Evidence from both behavioral and neuroscience studies shows that when people receive training on ways to perceive and represent their own fingers, they get better at doing so, which leads to higher mathematics achievement. The tasks we have developed for use in schools and homes (see below) are based on the training programs researchers use to improve finger-perception quality.
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  • The need for and importance of finger perception could even be the reason that pianists, and other musicians, often display higher mathematical understanding than people who don’t learn a musical instrument.
  • Teachers should celebrate and encourage finger use among younger learners and enable learners of any age to strengthen this brain capacity through finger counting and use. They can do so by engaging students in a range of classroom and home activities, such as:Give the students colored dots on their fingers and ask them to touch the corresponding piano keys:
  • Visual math is powerful for all learners. A few years ago Howard Gardner proposed a theory of multiple intelligences, suggesting that people have different approaches to learning, such as those that are visual, kinesthetic, or logical. T
  • To engage students in productive visual thinking, they should be asked, at regular intervals, how they see mathematical ideas, and to draw what they see. They can be given activities with visual questions and they can be asked to provide visual solutions to questions.
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    Great article on the strategies and rethinking of them in Math class for younger grades
Justin Medved

http://www.edu.gov.on.ca/eng/literacynumeracy/inspire/research/CBS_ThirdTeacher.pdf - 1 views

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    Designing the Learning Environment for Mathematics and Literacy, K to 8 Imagine the ideal learning environment for today's learner. What would it look like? Think about how much the world has changed in the last three decades and how rapidly it will continue to change in the years to come. How do we ensure that the instruction we provide is responsive to the shifting demands of the 21 st century? Researchers and practitioners in a wide range of disciplines - early childhood and developmental education, psychology and cognitive science, school architecture and design - maintain that the key to learning in today's world is not just the physical space we provide for students but the social space as well(Fraser, 2012; Helm et al., 2007; OWP/P Architects et al., 2010). The learning environment, they suggest, is "the third teacher" that can either enhance the kind of learning that optimizes our students' potential to respond creatively and meaningfully to future challenges or detract from it. Susan Fraser, for example, writes: "A classroom that is functioning successfully as a third teacher will be responsive to the children's interests, provide opportunities for children to make their thinking visible and then fosterfurtherlearning and engagement." (2012, p. 67)
mrdanbailey61

Inquiry is Differentiation | Discovering the Art of Mathematics (DAoM) - 2 views

  • explains some of the individual differences that influence problem solving
  • psychologist David Jonassen
  • Given the reality of all these differences, how can I even dream of a functional classroom in which every student is learning at their own learning edge?
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  • I believe that inquiry helps tremendously in reaching learners on different levels at the same time
  • work at their own pace
  • This is kind of funny because whole class discussions actually help make knowledge more equal which makes the classroom experience less differentiated. So while this is not really a tool to help students at their individual learning edges, it is a tool to bring out the differences and spread ideas and questions around the class.
    • mrdanbailey61
       
      This is a puzzle - how do we democratize input? This is why I like the idea of Twitter in the classroom - can be a way for reluctant speakers to particpate.
  • Ok, by now I know that it is impossible to find one particular task that will be just at the right level for all my students.
  • Another way of bringing in differentiation into your class is by letting students work on two different topics simultaneously. The students choose when they are ready to switch tasks for a while and then come back later to pick up the first topic again.
  • students know pretty well how they compare to other students and that they don’t like having to fit in and be the same all the time
  • Assessment and differentiation is a tricky subject,
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    I am not a math teacher, but I really like the ideas here. I am working at getting a handle on differentiation and inquiry-based learning for my subjects and classes (Our classes typically have 5-10 students with assessments and IEPs)..
garth nichols

Newman's prompts - 1 views

  • The Australian educator Anne Newman (1977) suggested five significant prompts to help determine where errors may occur in students attempts to solve written problems. She asked students the following questions as they attempted problems.1.       Please read the question to me. If you don't know a word, leave it out.2.       Tell me what the question is asking you to do.3.       Tell me how you are going to find the answer.4.       Show me what to do to get the answer. "Talk aloud" as you do it, so that I can    understand how you are thinking.5.       Now, write down your answer to the question.These five questions can be used to determine why students make mistakes with written mathematics questions.
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    Error analysis - how can we incorporate this into students final evaluation mark? Isn't having students understand their errors a key part in education? Maybe evaluation doesn't finish once you've handed the assignment/test back?
Marcie Lewis

Like Math? Thank Your Motivation, Not IQ: Scientific American - 1 views

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    Motivation is key to success learning mathematics.
mrdanbailey61

Framework for 21st Century Learning - P21 - 4 views

  • “21st century student outcomes”
  • are the skills, knowledge and expertise students should master to succeed in work and life in the 21st century.
  • Disciplines include: English, reading or language artsWorld languagesArtsMathematicsEconomicsScienceGeographyHistoryGovernment and Civics
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  • In addition to these subjects,
  • promoting understanding of academic content at much higher levels by weaving 21st century interdisciplinary themes into curriculum:
  • Global awareness Financial, economic, business and entrepreneurial literacy Civic literacy Health literacy Environmental literacy 
  • Learning and innovation skills increasingly are being recognized as the skills that separate students who are prepared for increasingly complex life and work environments in the 21st century, and those who are not.
  • A focus on creativity, critical thinking, communication and collaboration is essential to prepare students for the future.
  • To be effective in the 21st century, citizens and workers must be able to create, evaluate, and effectively utilize information, media, and technology.
  • Today's students need to develop thinking skills, content knowledge, and social and emotional competencies to navigate complex life and work environments. P21's essential Life and Career Skills include:: Flexibility & Adaptability Initiative & Self Direction Social & Cross-Cultural Skills Productivity & Accountability
  • Leadership & Responsibility
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    This page gives an overview of a framework for 21st century skills and learning. I like how it values all of the academic disciplines and gives links to different sites that focus on broader interdisciplinary themes, innovation skills, information, media, and technology skills, and life and career skills.
Justin Medved

Why the war over math is distracting and futile - The Globe and Mail - 2 views

  • The big questions on today’s blackboard is how to make math relevant for tomorrow,
  • “At the beginning of the 20th century, Latin was a required subject – it was seen as fundamental,” he says, to show how, as society changes, so does what it values. “By the end of century, Latin was gone. What will mathematics be by the end of this century?”
  • Dr. Small is showing a third option for two-number multiplication when a father raises his hand and asks: “But what’s the most efficient way?”“What’s your definition of efficient?” Dr. Small responds. “I think it’s probably the calculator.”
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  • But so it goes. The one side says, “drill and kill.” The other says “drill for skill.” Basically, though, just about every mathematician and math education researcher who was interviewed for this story agrees that the perfect math class should have a mix of skills and problem solving. They just can’t agree on the amounts of each, when to add them, and what to skip.
kcardinale

Python bumps off Java as top learning language | PCWorld - 0 views

  • Eight of the top 10 computer science departments now use Python to teach coding, as well as 27 of the top 39 schools
    • kcardinale
       
      What schools in Ontario are actually using Python to teach students computer science?
  • Java is frequently used in high school advanced courses, so the transition to Java in college is a natural one for students
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  • Java for computer science students and Python to teach programming skills for noncomputer science majors.
  • Other popular languages for teaching include MatLab, a mathematically oriented language often used to introduce scientists and engineers to programming. MatLab, however, seems to be increasingly supplanted by Java.
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    Interesting article that I just read, answering some computer science questions!
garth nichols

Our Makerspace: Inquiry & Challenges in Coding, Music & Mathematics - 0 views

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    As we explore STEM and engagement, here is an article about MakerEd that connects the two!
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