The Last Judgement Final 30% Evaluation Math Tasks & Tests

The Last Judgement

Final 30% Evaluation

Math Tasks & Tests

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

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

Siméon Poisson

[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

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

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

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

Falbo Clement

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

Thomas Dewar

SSR Final 30% Policy

Secondary Reform Program Planning &

Assessment New Report Card New Curriculum ...

Edubabble Summative Evaluation

judgements made at the end of a unit or course tests, tasks, etc. count in 70%

Final Evaluation subset of the above exams, tasks, etc. end of course only counts in 30%

Explicit Final 30% Practices

70% of mark = stuff during the course 30% of mark = stuff ‘toward the end’

last 3 weeks, 6@NEL 30% must suit

the course content what has gone before

No exemptions for 30%

Implicit Final 30% Practices ‘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

Implicit Final 30% Practices

‘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

a hunting story--taking things too explicitly

Covey’s & Guskey’s Laws Frustration--doing things the

same old ways but expecting different results. - Stephen Covey

Just because a thing is implemented poorly doesn’t mean it’s a bad idea. - Tom Guskey

Year End Crunch Issue

past practice: make & mark a comprehensive (big) written exam

current practice: big exam & assign big, long-term, take-home project causes crunch for students and staff

future practice: balance of reasonable exam & task(s) as appropriate

De-Crunchification

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

De-Crunchification 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)

De-Crunchification

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

Sample, revise, reduce as needed.

Ownership Issue Individual, not group work

may use groups, just mark individually ensure 30% reflects individuals’ work

Work during instructional time in-class rather than take-home (may

require simplification—good!) use school policy for absences

A camping story--‘overcomplexifying’

University Exams Issue 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”

Examining Exams Will a 25% exam not be taken

seriously? University alternative evaluations Preparation for life Preparation for university “Written tests or examinations, no

matter how well constructed, …” Richer mathematics x-

not simulation

Staff Learning Issue Acceptance Understanding

Using the ‘Edubabble’ Conceptual understanding Practicing Refinement/Mastery

Time/flexibility to practice & implement Staff Learning Opportunities

Question & Response

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

Context for Mathematics

May you live in interesting times.

Curse & Blessing

Mathematics Context Perceptions of mathematics Large-scale testing Curriculum Changes

Wider variety of teaching strategies Technology Richer curriculum Third math credit Double-cohort

Have You Ever Heard? “I’m no good at math.” “I’ve always hated math.” “I’m not a ‘math person’.” Why …

is illiteracy an issue but innumeracy a boast? is math perceived as irrelevant? do so many people feel this way about math?

Why? What about the next generation?

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

Grade 6 Attitudes 1999-2000

“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


EQAO Grade 9 Regional

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Applied Students Academic Students

HALTON ONTARIO


TIMSS-R Data (1999) Lessons stated are rote

learning/memorization-based Lessons developed work at

fundamental understanding


Halton Grade 9 EQAO Achievement Categories

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Amazing Graph Ahead! Can achievement category balance (not

score) impact overall achievement? The following scatter plot shows all HDSB

school EQAO results vs. ‘category balance’ Remember, this plot is not based on scores

in categories, just the relative balance (or imbalance) of achievement categories!


The Effect of Balanced or Traditional Practice on Overall Achievement

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0% 20% 40% 60% 80% 100%

Traditional Emphasis <---> Balanced Emphasis

All results are Academic, Level 3 & 4 combined

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(Comm+TIPS)/(KU+App)

A Richer Curriculum important part of every course is … inquiry important that students learn in a variety of ways

independently, cooperatively, with teacher direction through hands-on activities, and examples with

practice strategies used should vary

according to … needs learning is enhanced when

embedded in context

see p. 1

A Richer Curriculum rich environments open doors to big ideas process and content … are important knowledge becomes meaningful

and powerful in application skills should be introduced

as needed, in the contexts offered by various topics

importance ofcommunication

see p. 1

Full cognitive spectrum (Bloom’s) Well-rounded graduates

Citizens In the Workplace

Useful for feedback Used K-12 in Ontario Parents & students understand

A workshop unto itself!

More Rationale for Addressing All Achievement Categories

How to tell them apart? See p. 7

Math Expectations expand/simplify 2nd

degree equations apply principles of

probability to familiar situations describe nature of change in a

quadratic function determine the properties of similar

triangles through investigation

Balanced Practice See page 8

—’Pet Dwelling’ Moving along

the categories Each form is

needed in balance with the others

Remember

The Effect of Balanced or Traditional Practice on Overall Achievement

0

10

20

30

40

50

60

70

80

90

100

0% 20% 40% 60% 80% 100%

Traditional Emphasis <---> Balanced Emphasis

All results are Academic, Level 3 & 4 combined

Ov

era

ll A

ch

iev

em

en

t

(Comm+TIPS)/(KU+App)

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

Judgement Day Final Evaluation

Students & Staff Math teachers never die,

they just: go off on a tangent lose their identities tend to zero become angles lose their functions become irrational

St. Peter and the Math Teacher

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

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”?

A New CAST Rule? (see p. 6)

Rich Learning Tasks Review the tasks on pages 3 and 4 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?

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

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

Optional ‘But’ Toning “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

“But will my colleagues & classes like it?” new ideas can be challenging and healthy do they like unrich tasks and rote learning?

“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

Finding the Balance

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

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

Criteria for a High Quality Task

Refer to page 2 in the handout Apply to ‘package’ of tasks 1-4! Apply to ‘package’ of tasks 5-8! Use criteria when reviewing materials

in your course-specific groups

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

CHATT Sec Math Resources

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.

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.

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

It’s a stop sign! Fn-F3

STOP

It’s a boat! Fn-F3

TITANIC

It’s a pencil! Fn-F3

It’s a Santa! Fn-F3

1) parabola y = x2 – 2 with domain –1 to +1

2) circle x2 + (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, …

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

Markbook Mayhem

Inside every C+ student is a B- student trying to get out.

Art Peterson

Markbook Categories Setup (p. 9)

Mark Sets > Edit Weighting? Categories

Assigning Categories to Items

Categorize Weight

Assigning Multiple Categories (p. 9)

Categorize Weight Handy

Leveller (out of = 100)

File > Markbook Setup > Grades/Levels

“Weighty Matters” Discussion

Category, Entry or Equal Weight? Course Weightings?

What are your course components? How do you weight course components?

Component Weightings? How do you weight assignments?

Category Weightings

Wrap-Up

Closure should be seen as arriving at a new starting point.

- Gary Flewelling

6 da Vincian Principles Curiosità

an insatiably curios approach to life and an unrelenting quest for continuous learning

Dimostrazione a commitment to test knowledge through

experience, persistence and a willingness to learn through mistakes

Sensazione the continual refinement of the senses as the

means to enliven experience

6 da Vincian Principles Sfumato

a willingness to embrace ambiguity, paradox and uncertainty

Arte/Scienza development of the balance between science

and art, logic and imagination—’whole brain’ Connessione

a recognition of and appreciation forthe interconnectedness of all things and phenomena—systems thinking

Goal Setting Never tried a rich task?

Try one in the 70% (see CHATT) Done a few rich tasks?

Try more—especially in the 30% Doing LOTS of rich tasks?

be selective and balanced refine, streamline share the wealth

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 Silversee p. 1

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

Mao Zedong

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.

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

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 teachstudents to think forthemselves unless we too

think for ourselves. George Gadanidis

Top 10 Reasons To Skip Math Class

Thank You! Inspirational Ideas

Sandy DiLena Gary Flewelling George Gadanidis

Superb Support Jo-Anne Bryant Jocelyn Bryant Susan Orchard Math Heads

Premium Presenters Darren Luoma Kevin Spry

Thank You! 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

Thank You! Magnificent MDHS

Anne Colling Adrian DeGraaf Janice Gregory Ian Jones Debbie Majka Dean Murray Sheila Sheppard Nanci Wakeman-Jones Ron!

Picked Publishers Harcourt McGraw-Hill

Jeff CataniaSPS CoordinatorMath, e-Learning

School Programs, JWS 335-3665 x3250 CHATT or

[email protected]

October 11, 2002 10:30 – 11:30

Review final 30% materials—use p. 2 In course-based groups Please cooperate with wonderful facilitators!

1:00 – 3:30 Adapt or develop final 30% materials—use p. 5 Computers available (Sci. & Human. Clinics)

or Workshop (Luoma or Fry)

Tuesday Complete PD day evaluation on CHATT

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The Last Judgement Final 30% Evaluation Math Tasks & Tests