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The Last Judgement Final 30% Evaluation Math Tasks & Tests

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Agenda (page 1 ) n Explicit & Implicit Final 30% Practices n Implementation Issues n Question & Response n Context For Mathematics n Quality Tasks n Markbook Tricks n Resources n Plan for Rest of Day

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Life is good for only two things, discovering mathematics and teaching mathematics. Siméon Poisson

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[A misperception] about mathematics that we perpetrate in our classrooms is that the teacher knows the answer to any problem. This gives students the idea that there is a book somewhere with all the right answers, and that teachers know those answers. And if one could get hold of the book, one would have everything settled. That's so unlike the true nature of mathematics. Leon Henkin

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Only Socrates knew, after a lifetime of unceasing labor, that he was ignorant. Now every high-school student knows that. How did it become so easy? Allan Bloom

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Skills are to mathematics what scales are to music or spelling to writing. The objective of learning is to write, play music, or solve problems – not just master skills. National Research Council

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Why was six afraid of seven? Because 7 8 9! Falbo Clement

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Minds are like parachutes. They only function when they are open. Thomas Dewar

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SSR Final 30% Policy n Secondary Reform n Program Planning & Assessment n New Report Card n New Curriculum n...

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Edubabble n Summative Evaluation judgements made at the end of a unit or course tests, tasks, etc. count in 70% n Final Evaluation subset of the above exams, tasks, etc. end of course only counts in 30%

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Explicit Final 30% Practices n 70% of mark = stuff during the course n 30% of mark = stuff ‘toward the end’ last 3 weeks, 6@NEL n 30% must suit the course content what has gone before n No exemptions for 30%

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Implicit Final 30% Practices n ‘suit content & what’s gone before’ 30% reflects 70% (tasks/tests) 30% balanced by categories see KU/APP/TIPS/COMM term work balance course outline again provides guidance address key learnings, not every nitty- gritty-little specific expectation 30% is a variety of things rather than a single exam

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Implicit Final 30% Practices n ‘toward the end’ … can’t count term work in the 30% unit tests and unit summative tasks go in 70% last 3 weeks, last 6 for non-semestered n a hunting story--taking things too explicitly

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Covey’s & Guskey’s Laws n Frustration--doing things the same old ways but expecting different results. - Stephen Covey n Just because a thing is implemented poorly doesn’t mean it’s a bad idea. - Tom Guskey

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Year End Crunch Issue n past practice: make & mark a comprehensive (big) written exam n current practice: big exam & assign big, long-term, take-home project causes crunch for students and staff n future practice: balance of reasonable exam & task(s) as appropriate

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De-Crunchification n Simplifying Exam lighten reduce overlap with task portion balance categories and strands spread out marking grade 9’s may use EQAO address overall expectations, not every specific expectation

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De-Crunchification n Simplifying Tasks studying in traditional sense (e.g., memorizing facts/skills) not necessarily required focus on open-ended problem-solving do, but don’t overdo (e.g., huge, multi-week, …) coordinate with other staff using calendar (e.g., CHATT calendar of school final 30% dates)

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De-Crunchification n CHATT Sec Math > Sec Math Resources Sec Math > EQAO Gr 9 Math search, download final 30% materials adapt or use as is upload, share see next slide

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Sample, revise, reduce as needed.

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Ownership Issue n Individual, not group work may use groups, just mark individually ensure 30% reflects individuals’ work n Work during instructional time in-class rather than take-home (may require simplification—good!) use school policy for absences n A camping story--‘overcomplexifying’

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University Exams Issue n Ripley’s Believe it or Not OS:IS did not require a 40% exam (p. 67) “examinations shall constitute not less than 40 percent of the summative evaluation (see p. 22) for OACs” (p. 22) “summative evaluation may be based on: unit tests formal examinations standardized tests (which are related to course) projects “Written tests or examinations, no matter how well constructed, do not provide all of the information needed for a valid evaluation”

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Examining Exams n Will a 25% exam not be taken seriously? n University alternative evaluations n Preparation for life n Preparation for university n “Written tests or examinations, no matter how well constructed, …” n Richer mathematics x- not simulation

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Staff Learning Issue n Acceptance n Understanding Using the ‘Edubabble’ Conceptual understanding Practicing Refinement/Mastery n Time/flexibility to practice & implement n Staff Learning Opportunities

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Question & Response n Pass sticky note questions along n Last person in row please post n Please read p. 7-8 during collation n Response to posted questions n Open group question period

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Context for Mathematics May you live in interesting times. Curse & Blessing

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Mathematics Context n Perceptions of mathematics n Large-scale testing n Curriculum Changes Wider variety of teaching strategies Technology Richer curriculum Third math credit Double-cohort

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Have You Ever Heard? n “I’m no good at math.” n “I’ve always hated math.” n “I’m not a ‘math person’.” n Why … is illiteracy an issue but innumeracy a boast? is math perceived as irrelevant? do so many people feel this way about math? n Why? n What about the next generation?

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“Lies, damn lies, statistics.” - Benjamin Disraeli Grade 6 Attitudes 1999-2000

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“All you have to do is ask your friends about their experience with math to realize that for most people math is a negative experience, full of fear of forgetting rules, of making mistakes. Thinking is the last thing they associate with math.” - G. Gadanidis, 1999, Top 10 Reasons to Skip Math Class, p. 29

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“Lies, damn lies, statistics.” - Benjamin Disraeli EQAO Grade 9 Regional

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“Lies, damn lies, statistics.” - Benjamin Disraeli TIMSS-R Data (1999) n Lessons stated are rote learning/memorization-based n Lessons developed work at fundamental understanding

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“Lies, damn lies, statistics.” - Benjamin Disraeli Halton Grade 9 EQAO Achievement Categories

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“Lies, damn lies, statistics.” - Benjamin Disraeli Amazing Graph Ahead! n Can achievement category balance (not score) impact overall achievement? n The following scatter plot shows all HDSB school EQAO results vs. ‘category balance’ n Remember, this plot is not based on scores in categories, just the relative balance (or imbalance) of achievement categories!

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“Lies, damn lies, statistics.” - Benjamin Disraeli

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A Richer Curriculum n important part of every course is … inquiry n important that students learn in a variety of ways independently, cooperatively, with teacher direction through hands-on activities, and examples with practice n strategies used should vary according to … needs n learning is enhanced when embedded in context see p. 1

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A Richer Curriculum n rich environments open doors to big ideas n process and content … are important n knowledge becomes meaningful and powerful in application n skills should be introduced as needed, in the contexts offered by various topics n importance of communication see p. 1

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n Full cognitive spectrum (Bloom’s) n Well-rounded graduates Citizens In the Workplace n Useful for feedback Used K-12 in Ontario Parents & students understand n A workshop unto itself! More Rationale for Addressing All Achievement Categories

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How to tell them apart? See p. 7

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Math Expectations n expand/simplify 2nd degree equations n apply principles of probability to familiar situations n describe nature of change in a quadratic function n determine the properties of similar triangles through investigation

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Balanced Practice n See page 8— ’Pet Dwelling’ n Moving along the categories n Each form is needed in balance with the others n Remember

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What the good teacher has is not necessarily more knowledge than the student, but rather a superior competence to inquire and to be reflective. Joseph Schwad

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Judgement Day n Final Evaluation Students & Staff n Math teachers never die, they just: go off on a tangent lose their identities tend to zero become angles lose their functions become irrational n St. Peter and the Math Teacher

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Quality Tasks Education that consists of learning things and not the meaning of them is feeding upon the husks and not the corn. Mark Twain

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Brain Research “the human brain innately seeks to make meaning from and find relevance in its surroundings”, Renate, Cain (1994) do I “provide variety in my (final 30%) experiences” (e.g. context, technology, open- ended, rich tasks)? do “students actively create products/presentations (in 70%)” do I “encourage communication and divergent thinking”? do I “connect topics to prior topics, the real world and other subjects”?

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A New CAST Rule? (see p. 6)

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Rich Learning Tasks n Review the tasks on pages 3 and 4 n Discuss with a partner (& break) Compare task 1 with 5. Compare 2 and 6. Can you think of a course, topic or expectation addressed by tasks 3 or 4? Which types of problems are more often found in textbooks (i.e., tasks 1-4 or 5-8?) Which types of textbook problems do we typically assign? … avoid? Why? What fears might we have about rich learning tasks?

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Professionals are rarely, if ever, presented with a well-defined problem and expected to apply known methods to come up with an objective solution. Rather the task is most often presented to them in the rather vague and open-ended form of a “problematic situation”. Raffaella Borasi

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Optional ‘But’ Toning “But these tasks take too long, I have too much curriculum to cover.” tasks do address the curriculum & skills quality vs. quantity, go slow to go fast cover is an excellent word any single approach can be ineffective on its own, finding a balance is key “But I’ll miss some minor expectations and I have Johnny (future Ph.D.) & Mary, (future P.Eng.) in my class.” small % out of all students is “microscopia” a good diet for them? they will thrive on big ideas and rich tasks

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Optional ‘But’ Toning n “But what about the curriculum?” key learnings (overall expectations) summarize it students will learn it better in the long run rich tasks develop powerful learners n “But will my colleagues & classes like it?” new ideas can be challenging and healthy do they like unrich tasks and rote learning? n “But my class will fail common tests/exams?” ensure you have input into these make rich tasks a part of the evaluations find a balance that works for you

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Finding the Balance n Practising skills is part of mathematics, it shouldn’t be mathematics facts and procedures problem-solving understanding George Gadanidis, Top 10 Reasons to Skip Mathematics, p. 18

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Students who memorize facts or procedures without understanding often are not sure when or how to use what they know, and such learning is often quite fragile. Bransford, Brown and Cocking

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Criteria for a High Quality Task n Refer to page 2 in the handout n Apply to ‘package’ of tasks 1-4! n Apply to ‘package’ of tasks 5-8! n Use criteria when reviewing materials in your course-specific groups

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Assessment Tools n Rubrics, Scales, Checklists, Schemes n Rich Learning Tasks n Other Materials

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CHATT Sec Math Resources

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Top 10 Report Card Comments You Just Can’t Get Away With 6. Chances for success are slim to none (and Slim just left town!) 7. Living proof that nature does not abhor a vacuum. 8. The wheel is spinning but the hamster's gone. 9. If you give him a penny for his thoughts, you get change back. 10. A few fries short of a Happy Meal.

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Top 10 Report Card Comments You Just Can’t Get Away With 1. The gates are down, the lights are flashing, but the train just isn't coming! 2. Has an IQ of 2, and it takes 3 to grunt. 3. So dense, light bends around her. 4. If brains were taxed, he'd get a rebate. 5. If what you don't know can't hurt you, she's practically invincible.

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Win, Lose or Draw n grab a pencil/pen n prepare to draw n no repetition of instructions will occur n listen carefully n only one guess allowed per person n two halves of room compete for fun n winners gets big prizes (of course!) n Fn-F3

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It’s a stop sign! Fn-F3 STOP

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It’s a boat! Fn-F3 TITANIC

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It’s a pencil! Fn-F3

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It’s a Santa! Fn-F3 1)parabola y = x 2 – 2 with domain –1 to +1 2)circle x 2 + (y-4) 2 = ¼ 3)Transform first parabola by +1 (leaving original copy) then multiply by factor of.5, use domain – ½ to +½ 4)Draw equilateral triangle with sides length 2 so top vertex touches bottom of circle, fill in red, …

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Skills are to mathematics what scales are to music or spelling to writing. The objective of learning is to write, play music, or solve problems – not just master skills. National Research Council

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Markbook Mayhem Inside every C+ student is a B- student trying to get out. Art Peterson

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Markbook Categories Setup (p. 9) n Mark Sets > Edit n Weighting? n Categories

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Assigning Categories to Items n n Categorize n Weight

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Assigning Multiple Categories (p. 9) n n Categorize n Weight n Handy Leveller (out of = 100) n File > Markbook Setup > Grades/Levels

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“Weighty Matters” Discussion n Category, Entry or Equal Weight? n Course Weightings? What are your course components? How do you weight course components? n Component Weightings? How do you weight assignments?

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Category Weightings

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Wrap-Up Closure should be seen as arriving at a new starting point. - Gary Flewelling

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6 da Vincian Principles n Curiosità an insatiably curios approach to life and an unrelenting quest for continuous learning n Dimostrazione a commitment to test knowledge through experience, persistence and a willingness to learn through mistakes n Sensazione the continual refinement of the senses as the means to enliven experience

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6 da Vincian Principles n Sfumato a willingness to embrace ambiguity, paradox and uncertainty n Arte/Scienza development of the balance between science and art, logic and imagination—’whole brain’ n Connessione a recognition of and appreciation for the interconnectedness of all things and phenomena—systems thinking

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Goal Setting n Never tried a rich task? Try one in the 70% (see CHATT) n Done a few rich tasks? Try more—especially in the 30% n Doing LOTS of rich tasks? be selective and balanced refine, streamline share the wealth

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n Clarion calls exhorting teachers to better practice and elegant materials showing the way will all be fruitless if those involved in mathematics—students, teachers, administrators, parents and politicians—see no reason to change. Jeremy Kilpatrick & Edward Silver see p. 1

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Our attitude toward ourselves should be “to be insatiable in learning” and towards others “to be tireless in teaching.” ø Mao Zedong

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n Most reform movements do not value teacher knowledge. They often rely on arbitrary ideas, on formulas, on rules that someone else makes up. They often treat teacher knowledge as a problem and not as the solution. n The real curriculum, the curriculum that has a lasting, positive effect on students is not determined by expectations, achievement charts, or other rules and regulations-- anymore than real mathematical thinking is determined by rules and procedures. I think that the teacher is the real curriculum. p. 1

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n The only hope for improving what happens in math classrooms is that teachers and parents trust what they know is best for students. That they not follow in the footsteps of others. That they not conform to the status quo. That they think for themselves. We cannot teach students to think for themselves unless we too think for ourselves. n George Gadanidis Top 10 Reasons To Skip Math Class

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Thank You! n Inspirational Ideas Sandy DiLena Gary Flewelling George Gadanidis n Superb Support Jo-Anne Bryant Jocelyn Bryant Susan Orchard Math Heads n Premium Presenters Darren Luoma Kevin Spry

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Thank You! n Fantastic Facilitators Nancy Anstett Clare Balch Susan Carrigan Danielle DeSantis Sandy DiLena Lloyd Gough Sally Gray Susan Holland Garry Kiziak Amy Lin Allyson Miller Ian Newell John Prince Robyn Strange

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Thank You! n Magnificent MDHS Anne Colling Adrian DeGraaf Janice Gregory Ian Jones Debbie Majka Dean Murray Sheila Sheppard Nanci Wakeman-Jones Ron! n Picked Publishers Harcourt McGraw-Hill

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Jeff Catania SPS Coordinator Math, e-Learning School Programs, JWS 335-3665 x3250 CHATT or cataniaj@hdsb.ca

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October 11, 2002 n 10:30 – 11:30 Review final 30% materials—use p. 2 In course-based groups Please cooperate with wonderful facilitators! n 1:00 – 3:30 Adapt or develop final 30% materials—use p. 5 Computers available (Sci. & Human. Clinics) or Workshop (Luoma or Fry) n Tuesday Complete PD day evaluation on CHATT

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