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Logically Speaking

Logically Speaking . November 19, 2016. Opening activity. Frog jumping puzzle

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Logically Speaking

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  1. Logically Speaking November 19, 2016

  2. Opening activity • Frog jumping puzzle • -  The seven rocks are laid out in a horizontal line and numbered left to right.  The six frogs are evenly divided into a green trio and a yellow trio.  The green frogs sit on Rocks 1, 2, and 3, facing right.  The yellow frogs sit on Rocks 5, 6, and 7, facing left.  Rock 4 is vacant.  • The challenge is to transpose the trios, jumping the green frogs to Rocks 5, 6, and 7 and the yellow frogs to Rocks 1, 2, and 3.  Their movement is restricted.  A frog can only jump forward, either hopping to a vacant rock one place ahead or leaping over its neighbor frog to a vacant rock two places ahead. • (If you get this accomplished, try Fractional Triangles or Eight Hidden squares)

  3. Expectations of the day

  4. Agenda • Frog puzzle opener • Engaging the learner – promoting learning • Teachers as unlearners • Facilitators of the future - stations • Math practices meet 21st century • Open middle tasks • Get it together • Challengers King Arthur • Final discussionand evaluation

  5. Engaging the learner – How do we promote learning • Discuss at your table powerful learning experiences and what might have been the characteristics of that environment (include when you were a teacher but also when you were a student)

  6. Teacher-Reported Conditions That Promote Powerful Learning (p. 20 From Master Teacher to Master Learner) • Safe learning environment • Personal Investment • Real-word application • Fun • Relevance to their lives • Social • Interesting questions • Positive learning environment • Real audience • Passion • Teachers and mentors • Feedback • Autonomy and agency • Challenging • Cross-disciplines • Not time constrained • Flow From Master Teacher to Master Learner By Will Richardson, pg 20

  7. Teachers as unlearners: Refute each of these assumptions as a mathematician (reference pages 37-41) • We are the smartest people in the room • We have to organize everything • We can do without technology • Everything that kids do is quantifiable • We should only ask questions with a definite or known answer • Curriculum is the main driver of learning

  8. Skills that are not curricular

  9. Questioning techniques • Take about 3 minutes to review the questioning suggestions without discussion. • Highlight those questions that you feel would generate deeper discussions in your classroom. • After 3 minutes, I will group you with members of another group to discuss which questions you feel are most valuable. We will be applying your decisions shortly! • I love this quote: “If a student indicates that she/he does not know the answer, we can ask, “Pretend you did know the answer – what words would come out of your mouth? “ “ Rick Wormeli

  10. Tasks that grouping is engaging (Station 1) • Get it together rules • Each member gets a clue • Each member can only look at their own clue • Each member can tell about their clue but not show others • If you have a question, ask your team and if they don’t know, ask the teacher • Everyone participates • Listen to each other • Give reasons for your thinking • Ask for other opinions

  11. Practice – open middle problems – (Station 2) Open middle tasks are low floor, high ceiling. That means that students usually understand what is being asked of them. Getting solution, however, can be challenging.

  12. Mathematical practices meet the 21st century (Station 3)

  13. King Arthur’s Problem – (Station 4) This is a fictionalized historical problem. King Arthur wanted to decide who was the fittest to marry his daughter and chose this method. When all his knights were seated at the round table, he entered the room, pointed to the first knight and said: “You live.” The knight seated next wasn’t as fortunate. “You die,” said King Arthur, chopping off his head. To the third knight he said: “You live,” and to the fourth, he said: “You die,” chopping off his head. He continued doing this around the circle, chopping off the head of every other knight, until just one was left. This remaining knight got to marry his daughter, but, as legend goes, he was never quite the same again. Where would you sit in order to live? Determine the best seat in the house if there were 30, 31 or 32 knights. See if you can determine a pattern and predict the best seat for any number of knights.

  14. Station time • Each station will last 15 minutes. • Once you have completed 2 stations, there will be a five minute break. • After the break, the final 2 stations will be completed. • As you work through each station, determine what is most useful for the students you serve and how the practice generated can be applied next week. • Make sure you are using your questioning choices when you are the facilitator. • Remember, all are probably learning something new. Mistakes provide opportunities for even more learning!

  15. Closing discussion and evaluation • Part 4: Letting go • We have many standards that we are expected to facilitate for mastery. We know, however, that employers want problem solvers and creative thinkers. How do we restructure to allow for more student direction and choice? • Physical structure • Time • Lesson planning • Assessment • Personal challenges (create your own): • I like to have a daily plan prepped and ready so my goal is ……

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