PROBLEM #1 If 6 cats can kill 6 rats in 6 minutes, how many cats are needed to kill 100 rats in 50 minutes? http://commons.wikimedia.org/wiki/File:Claw.jpg
PROBLEM #1 If 6 cats can kill 6 rats in 6 minutes, how many cats are needed to kill 100 rats in 50 minutes? 200? 13? 12? 50?...? http://commons.wikimedia.org/wiki/File:Husky_rat.jpg
WELCOME this is going to be different challenge opportunity thank you facilitators this is going to be different challenge opportunity
ROUGH AGENDA Morning do some problems discuss them small group discussion led by facilitator Afternoon do an active read discuss it presentation small group discussion led by facilitator question/answer
PROBLEM #2 Corner-to-Corner need 9 volunteers at every site!
PROBLEM #4 Four cards (A, 3, 2, 4) put top card face up on the table move next card to the back of the stack repeat Five cards? Six cards?...
GROUP DISCUSSION What skills would students need in order to successfully complete these tasks or tasks like them? Do not constrain yourself to mathematical pre- requisite knowledge – although that is important. Attend also to meta-skills such as willingness to take risks, etc. ENJOY YOUR LUNCH!
LOCKHART'S LAMENT * Do an active read of Lockhart's Lament: read it discuss it – line by line – paragraph by paragraph – section by section – whole piece underline and highlight things of interest and importance
LOCKHART'S LAMENT * Wouldn't it be nice if these were the main goals of mathematics education (3 rd to last paragraph)? Wouldn't it be nice if these were the types of students we were able to produce (2 nd to last paragraph)? Wouldn't it be nice if curriculum was, indeed, constructed to encourage this sort of classroom atmosphere (last paragraph)?
GOALS FOR STUDENTS - PSAI: page 4 - The main goals of mathematics education are to prepare students to... Students who have met these goals... In order to assist students in attaining these goals, teachers are encouraged to develop a classroom atmosphere that fosters conceptual understanding through...
MATHEMATICAL PROCESSES - PSAI: page 6 - Students are expected to: 1.use communication in order to learn and express their understanding [C] 2.make connections among mathematical ideas, other concepts in mathematics, everyday experiences and other disciplines [CN] 3.demonstrate fluency with mental mathematics and estimation [ME] 4.develop and apply new mathematical knowledge through problem solving [PS] 5.develop mathematical reasoning [R] 6.select and use technology as a tool for learning and for solving problems [T] 7.develop visualization skills to assist in processing information, making connections and solving problems [V]
MATHEMATICAL PROCESSES - PSAI: page 6 - The seven mathematical processes are critical aspects of learning, doing and understanding mathematics. Students must encounter these processes regularly in a mathematics program in order to achieve the goals of mathematics education. All seven processes should be used in the teaching and learning of mathematics. Each specific outcome includes a list of relevant mathematical processes. The identified processes are to be used as a primary focus of instruction and assessment.
WHERE IS THIS COMING FROM? WNCP, NCTM, UKS, WACF,... Predicated on the theory that humans learn with and from: experiences discourse thinking
SHIFT IN CURRICULUM the GOALS FOR STUDENTS and the MATHEMATICAL PROCESSES is now the content of the curriculum the SPECIFIC OUTCOMES is now the context in which the content is covered content vs. context
FOR EXAMPLE - corner to corner - 10C – Relations and Functions (PSAI – page 25) 4. Describe and represent linear relations, using: words ordered pairs tables of values graphs equations [C, CN, R, V] +[PS]
WHAT NEEDS TO CHANGE? how we look at curriculum – content vs. context students – need to think and be active participants in their learning... (NEW TO THEM TOO!) classroom – environment, culture, norms teaching – stop letting student opt out of thinking – start helping students learn how to think
STOP LETTING STUDENT OPT OUT OF THINKING way in which we answer questions types of questions we ask how often we level pre-requisite knowledge the way we give and use notes deficit model of students assessment
START HELPING STUDENTS LEARN HOW TO THINK 7 processes are thinking skills teach them model them scaffold them value them (evaluate them)
BUILD YOUR OWN LIGHTSABER - examples from the edge - boardwork random groups upside down lesson student generated notes partner quizzes group tests http://commons.wikimedia.org/wiki/File:Lightsabers.png
GROUP DISCUSSIONS What are the things about the new curriculum you find the most exciting? What are the things you find most troubling? What are the things you find most challenging? If you could ask Peter one question what would it be?