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Pre-Cal 40S Slides March 19, 2008
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Darren Kuropatwa
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The sum and difference identities. More pythagorean identities and a quiz.
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Pre-Cal 40S Slides March 24, 2008
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Recommandé
The sum and difference identities. More pythagorean identities and a quiz.
Pre-Cal 40S Slides October 24, 2007
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Emblem results
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Introduction to the sum and difference identities: The Sine Dance!
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The double angle identities.
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Trig.ppt for Video
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Proof on Sum and Difference of Trigonometric Identities
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Behind Their Eyes - making thinking visible is not enough Walk into any classroom and watch the breakneck pace at which teachers are working hard to help students learn. Mind you, if we don’t uncover what students are thinking while learning, they may be running down the wrong path. OK, so we need ways to make student thinking visible. Seeing their thinking is important, but we also need to create the time and space for teachers to absorb, reflect, and act on what their students thinking reveals. This workshop shares strategies both for making student thinking visible and for creating time and space for teachers to meaningfully act on what they learn about what’s going on behind their eyes.
Behind Their Eyes v1
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“If you really want to understand something, try changing it.” - Kurt Lewin As the Director of Learning for a school division made up of 18 schools, my job is to help lead the largest change initiative ever undertaken in our school community. One of the most important, difficult, messy things any school leader does is lead change. While we can learn from the change leadership of others, copying their work most often leads to failure. Success is more likely to come from adapting others work to our own context. In this workshop I share the journey we’ve undertaken collectively in our schools; how we developed a shared vision, cultivated collaborative cultures, maintained a focus on deep learning, and wrestle with the nuances of accountability. Informed by the latest research on change management in education, we also model strategies for fostering deep learning conversations in your schools. We’ll engage in some deeper learning conversations together and take back a wealth of ideas you can adapt to your own context. Developing collaborative cultures is careful and precise work that has profound impact when carried out well. So how do you do that? Come, let’s learn together. Good people are important, but good cultures are moreso.
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Presented at the Richmond District Conference, Feb 2017. Why does digital learning matter? In a society that is increasingly technophilic what are the new literacies we need to be aware of for our own learning and that of our students? How does this impact the way we think about and teach our children to become empowered and empathetic responsible citizens? Answers to these questions and more are shared through a series of powerful tales of learning.
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Presented at the Richmond District Conference, Feb 2017. A series of stories woven together to start a conversation with middle and high school students, teachers, and parents about living our lives on and offline (on The Fourth Screen) more thoughtfully. This talk focuses primarily on the ideas of Empathy, Empowerment & Persistent Kindness and shares resources teachers can use to lead these sorts of conversations with their own students.
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Slides to support a master class on making student thinking visible through practical hands-on activities and structured around Dylan Wiliam's work on formative assessment and active learning. Held at the BYTE Conference 2017 in Portage la Prairie, Manitoba.
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Darren Kuropatwa
In a world where knowledge is more a verb than a noun how do we foster deep learning in our students? Good questions cause thinking. Unfortunately, many of the questions regularly asked in classrooms focus on knowledge as a noun. This presentation will explore the effective use of thinking and learning tools in the classroom. We will work together to model teaching practices that lead to students co-constructing a networked (real world) rather than hierarchical (artificial) understanding of their world regardless of grade level or discipline. Participants leave this workshop with a toolkit of research based questioning and thinking strategies they can begin using with their students tomorrow.
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A series of stories woven together to start a conversation with middle and high school students about living our lives on and offline (on The Fourth Screen) more thoughtfully. This talk focuses primarily on the ideas of Empathy, Empowerment & Persistent Kindness and shares resources teachers can use to lead these sorts of conversations with their own students.
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Behind Their Eyes - making thinking visible is not enough Walk into any classroom and watch the breakneck pace at which teachers are working hard to help students learn. Mind you, if we don’t uncover what students are thinking while learning, they may be running down the wrong path. OK, so we need ways to make student thinking visible. Seeing their thinking is important, but we also need to create the time and space for teachers to absorb, reflect, and act on what their students thinking reveals. This workshop shares strategies both for making student thinking visible and for creating time and space for teachers to meaningfully act on what they learn about what’s going on behind their eyes.
Behind Their Eyes v1
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Darren Kuropatwa
“If you really want to understand something, try changing it.” - Kurt Lewin As the Director of Learning for a school division made up of 18 schools, my job is to help lead the largest change initiative ever undertaken in our school community. One of the most important, difficult, messy things any school leader does is lead change. While we can learn from the change leadership of others, copying their work most often leads to failure. Success is more likely to come from adapting others work to our own context. In this workshop I share the journey we’ve undertaken collectively in our schools; how we developed a shared vision, cultivated collaborative cultures, maintained a focus on deep learning, and wrestle with the nuances of accountability. Informed by the latest research on change management in education, we also model strategies for fostering deep learning conversations in your schools. We’ll engage in some deeper learning conversations together and take back a wealth of ideas you can adapt to your own context. Developing collaborative cultures is careful and precise work that has profound impact when carried out well. So how do you do that? Come, let’s learn together. Good people are important, but good cultures are moreso.
Leading Change v1
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Darren Kuropatwa
In a world where knowledge is more a verb than a noun how do we foster deep learning in our students? Good questions cause thinking. Unfortunately, many of the questions regularly asked in classrooms focus on knowledge as a noun. This presentation will explore inquiry as a pedagogical stance and the effective use of thinking and learning tools in the classroom. We will work together to model teaching practices that lead to students co-constructing a networked (real world) rather than hierarchical (artificial) understanding of their world regardless of grade level or discipline. Participants will leave this workshop with a toolkit of research based questioning and thinking strategies they can begin using with their students tomorrow.
Providing Permission To Wonder v2.1
Providing Permission To Wonder v2.1
Darren Kuropatwa
This participatory session will engage attendees in some meaningful dialogue around several aspects of digital citizenship. We'll explore some hot-button topics and consider their impact on the work we do as educators. This session will provide clarification around a number of key digital citizenship issues and will also highlight a valuable model for engaging your students in classroom conversations. There’s a fair bit of fear mongering disguised as digital citizenship online. Our kids need more models of empathy and empowerment – so do we. We’ll share some of those models too.
Things That Suck About Digital Citizenship v1
Things That Suck About Digital Citizenship v1
Darren Kuropatwa
Presented at the Riding the Wave Conference in Gimli, Manitoba. May 2017. In two words, you remember the whole story: glass slipper, sour grapes, cold porridge. You remember more than facts, you recall relationships & deeper connections between characters. Some of the powerful ways we leverage digital for deeper learning includes challenging sources of information (fake news), exploring bias (developing empathy through multiple perspectives), and creating powerful feedback loops that foster deeper learning. Powerful narratives, in a word or two, bring to mind a wealth of ideas & relationships; more than just facts. How can we find stories that make our teaching sticky and help kids find, and more importantly tell, stories that make learning stick? This workshop will equip teachers with the skills & knowledge to foster deeper learning across the curriculum by intentionally leveraging digital tools to foster deeper learning.
Digital Storytelling for Deeper Learning v1
Digital Storytelling for Deeper Learning v1
Darren Kuropatwa
Presented at the Richmond District Conference, Feb 2017. Why does digital learning matter? In a society that is increasingly technophilic what are the new literacies we need to be aware of for our own learning and that of our students? How does this impact the way we think about and teach our children to become empowered and empathetic responsible citizens? Answers to these questions and more are shared through a series of powerful tales of learning.
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Darren Kuropatwa
Presented at the Richmond District Conference, Feb 2017. A series of stories woven together to start a conversation with middle and high school students, teachers, and parents about living our lives on and offline (on The Fourth Screen) more thoughtfully. This talk focuses primarily on the ideas of Empathy, Empowerment & Persistent Kindness and shares resources teachers can use to lead these sorts of conversations with their own students.
The Fourth Screen v4.2
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Slides to support a master class on making student thinking visible through practical hands-on activities and structured around Dylan Wiliam's work on formative assessment and active learning. Held at the BYTE Conference 2017 in Portage la Prairie, Manitoba.
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Darren Kuropatwa
A group of educators from the BYTE Conference 2017 (Build Your Teaching Experience) share their ideas about learning as a series of visual metaphors they found on their phones.
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Darren Kuropatwa
Slides to support a Keynote presentation to Early Years and Middle Years teachers in Hanover School Division on 3 February 2017.
Leveraging Digital for Deeper Learning
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Darren Kuropatwa
Slides to support a master class at the PRIZMAH Conference in Chicago, IL. 5 Feb 2017. How can we make learning sticky using powerful storytelling frameworks that tap into peoples' emotions? How do we involve all students in creating digital content that doesn't also create hours of content for teachers to assess? This interactive session will showcase Digital Storytelling activities teachers can use in class tomorrow! Document student learning & foster reflective ways for students to share their learning. 1st: we play! Then we'll discuss how to practically adapt these ideas, make them your own, and figure out what sort of infrastructure needs to be in place to support these kinds of powerful learning experiences. We’ll learn how to exercise your students' & your own creativity muscles and share simple strategies for collecting & publishing student work.
We Learn Through Stories at PRIZMAH17
We Learn Through Stories at PRIZMAH17
Darren Kuropatwa
In a world where knowledge is more a verb than a noun how do we foster deep learning in our students? Good questions cause thinking. Unfortunately, many of the questions regularly asked in classrooms focus on knowledge as a noun. This presentation will explore the effective use of thinking and learning tools in the classroom. We will work together to model teaching practices that lead to students co-constructing a networked (real world) rather than hierarchical (artificial) understanding of their world regardless of grade level or discipline. Participants leave this workshop with a toolkit of research based questioning and thinking strategies they can begin using with their students tomorrow.
Providing Permission to Wonder v3
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Darren Kuropatwa
A series of stories woven together to start a conversation with middle and high school students about living our lives on and offline (on The Fourth Screen) more thoughtfully. This talk focuses primarily on the ideas of Empathy, Empowerment & Persistent Kindness and shares resources teachers can use to lead these sorts of conversations with their own students.
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Slides to support a master class on making student thinking visible through practical hands-on activities and structured around Dylan Wiliam's work on formative assessment and active learning.
Making Student Thinking Visible v3.7
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Darren Kuropatwa
In a world where knowledge is more a verb than a noun how do we foster deep learning in our students? Good questions cause thinking. Unfortunately, many of the questions regularly asked in classrooms focus on knowledge as a noun. This presentation will explore the effective use of thinking and learning tools in the classroom. We will work together to model teaching practices that lead to students co-constructing a networked (real world) rather than hierarchical (artificial) understanding of their world regardless of grade level or discipline. Participants leave this workshop with a toolkit of research based questioning and thinking strategies they can begin using with their students tomorrow.
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Darren Kuropatwa
A series of stories woven together to start a conversation with middle and high school students about living our lives on and offline (on The Fourth Screen) more thoughtfully. This talk focuses primarily on the ideas of Empathy, Empowerment & Persistent Kindness and shares resources teachers can use to lead these sorts of conversations with their own students.
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A group of educators at the Building Learning Communities Conference share their ideas about learning as a series of visual metaphors.
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Slides to support a master class at the Building Learning Communities Conference in Boston, MA. 18 July 2016. How can we make learning sticky using powerful storytelling frameworks that tap into peoples' emotions? How do we involve all students in creating digital content that doesn't also create hours of content for teachers to assess? This interactive session will showcase Digital Storytelling activities teachers can use in class tomorrow! Document student learning & foster reflective ways for students to share their learning. 1st: we play! Then we'll discuss how to practically adapt these ideas, make them your own, and figure out what sort of infrastructure needs to be in place to support these kinds of powerful learning experiences. We’ll learn how to exercise your students' & your own creativity muscles and share simple strategies for collecting & publishing student work.
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Behind Their Eyes v1
Behind Their Eyes v1
Leading Change v1
Leading Change v1
Providing Permission To Wonder v2.1
Providing Permission To Wonder v2.1
Things That Suck About Digital Citizenship v1
Things That Suck About Digital Citizenship v1
Digital Storytelling for Deeper Learning v1
Digital Storytelling for Deeper Learning v1
Tales of Learning and the Gifts of Footprints v4.2
Tales of Learning and the Gifts of Footprints v4.2
The Fourth Screen v4.2
The Fourth Screen v4.2
Making Student Thinking Visible v4
Making Student Thinking Visible v4
Learning is at BYTE 2017
Learning is at BYTE 2017
Leveraging Digital for Deeper Learning
Leveraging Digital for Deeper Learning
We Learn Through Stories at PRIZMAH17
We Learn Through Stories at PRIZMAH17
Providing Permission to Wonder v3
Providing Permission to Wonder v3
The Fourth Screen v4.1
The Fourth Screen v4.1
Making Student Thinking Visible v3.7
Making Student Thinking Visible v3.7
Learning is at AUHSD
Learning is at AUHSD
Providing Permission to Wonder v2
Providing Permission to Wonder v2
The Fourth Screen v4
The Fourth Screen v4
Learning is at BLC16
Learning is at BLC16
We Learn Through Stories v4 (master class)
We Learn Through Stories v4 (master class)
Deep Learning Design: the middle ring
Deep Learning Design: the middle ring
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Andreas Schleicher, Director for Education and Skills at the OECD, presents at the webinar No Child Left Behind: Tackling the School Absenteeism Crisis on 30 April 2024.
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God is a creative God Gen 1:1. All that He created was “good”, could also be translated “beautiful”. God created man in His own image Gen 1:27. Maths helps us discover the beauty that God has created in His world and, in turn, create beautiful designs to serve and enrich the lives of others.
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In BC’s nearly-decade-old “new” curriculum, the curricular competencies describe the processes that students are expected to develop in areas of learning such as mathematics. They reflect the “Do” in the “Know-Do-Understand” model. Under the “Communicating” header falls the curricular competency “Explain and justify mathematical ideas and decisions.” Note that it contains two processes: “Explain mathematical ideas” and “Justify mathematical decisions.” I have broken it down into its separate parts in order to understand--or reveal--its meaning. The first part is commonplace in classrooms. By now, BC math teachers—and students—understand that “Explain mathematical ideas” means more than “Show your work.” Teachers consistently ask “What did you do?” and “How do you know?” This process is about retelling, not just of steps but of thinking. The second part happens less frequently. Think back to the last time that you observed a student make—a necessary precursor to justify—a mathematical decision. “Justify” is about defending. Like “explain,” it involves reasoning; unlike “explain,” it also involves opinion and debate. In order to reinterpret the curricular competency “Explain and justify mathematical ideas and decisions,” I will continue to take apart its constituent part “Justify mathematical decisions” and carefully examine the term “mathematical decisions.” What, exactly, is a “mathematical decision”? Below, I will categorize answers to this question. These categories, and the provided examples, may help to suggest new opportunities for students to justify.
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1.
The Sine Dance
... it goes something like this ... ganga flow
2.
Prove each of
the following identities ...
3.
Prove each of
the following identities ...
4.
Prove each of
the following identities ...
5.
The Sum and
Difference Identities Notice the patterns and get ready to dance ... the Sine Dance! IMAGES (c) JANN
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