Transcript Slide 1

Professional Learning
for Mathematics
Leaders and Coaches—
Not just a 3-part series
Day 3
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What’s My Number?
• Multiply the number of brothers you
have by 2
• Add 3
• Multiply by 5
• Add the number of sisters you have
• Multiply by 10
• Add the number of living grandparents
• Subtract 150
Your number is: ____ ____ ____
# of
brothers
# of
sisters
# of
grandparents
Inside/Outside Circle
• Each person from your board go to one
of the four corners
1 min discussion
• Share an interesting aspect from the
‘view & discuss’ or ‘do’ that you
participated in.
• How are the Big Ideas impacting your
practice?
• Which is more comfortable for you:
Open or Parallel Tasks, and why?
• How are you using the MATCH Template
and/or PPQT to help you with lesson
planning?
Provincial-level Evidence
Trends in Provincial EQAO Math
Point increase per year
over the past 3 years
90
% at Provincial Standard
80
2.00 in 9 Academic
70
1.00 in Grade 3
60
1.66 in Combined 9
50
0.66 in Grade 6
40
1.00 in 9 Applied
30
20
10
0
1
2
3
2004-2009
4
5
Provincial-level Evidence
% at Provincial Standard
Provincial Grade 9 EQAO Data
100
80
60
Rate = 1.4 points per semester
increasing
Rate = 2.3 points per semester
40
20
Rate = 1.6 points per semester
increasing
Rate = 2 points per semester
0
Applied
Academic
1
3
5
7
Semesters 2004-09
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Board-level Evidence and BIPs
• Halton DSB’s 2009-10 Math GAINS
Transition Project paper
• Peterborough Victoria Northumberland
Clarington CDSB 2-part roving Math
GAINS report
• Greater Essex CDSB roving Math GAINS
report
Next Steps – Materials
• WINS = Winning with Instructional Navigation
Supports
• Grade bands K-1, 2-3, 4-5, 6-7, 7-8, ?-?
• Focused on Number Sense
• “Thinking Book” for learners and “guide” for
learning facilitators
• Could be used at home use, but good for many
other applications
• 3-part lessons with 4 parallel questions
addressing the same learning goal
• multiple solutions with scaffolding questions
Next Steps – Professional Learning
• Sessions January to June 2010 with possible
themes:
– WINS
– Managing Group Dynamics in Classrooms and
Schools
– Strategic planning work sessions
• Access customized provincial-level support
through Jeff Irvine, Myrna Ingalls, Demetra
Saldaris
• Regular postings on www.edugains.ca
Addressing Questions from
Session 2
Scaffolding Thinking Prompts
• We ask an open question.
• Nobody responds.
• One thing we need to work on
are strategies to use in that
situation.
Let’s try an example.
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Scaffolding Thinking Prompts
• Let’s start with one of the
open questions from last
session.
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Scaffolding Thinking Prompts
Open Question:
Create two linear growing
patterns that are really similar.
• How are they similar?
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Scaffolding Thinking Prompts
Open Question:
Create two linear growing patterns that are
really similar. How are they similar?
• Could one of your patterns be
1, 4, 9, 16,…? Explain.
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Scaffolding Thinking Prompts
Open Question:
Create two linear growing patterns that are
really similar. How are they similar?
• If you were describing your
pattern to another student, what
information would you give them?
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Scaffolding Thinking Prompts
Open Question:
Create two linear growing patterns that are
really similar. How are they similar?
• Are 2, 5, 8, 11, 14,… and
5, 10, 15, 20,… really similar?
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Discuss at your table:
How do the three questions help students
with scaffolding their thinking to answer
the open question?
Open Question:
Create two linear growing patterns that are
really similar. How are they similar?
How does the Big Idea and
the Lesson Goal impact the
questions you are asking
for scaffolding?
Another example from last time
• Which two graphs do you
think are most alike? Why?
Y = 3x2 – 2
y = -3x2 – 2
Y = 2x2 + 3
y = 3x2 + 2
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Scaffolding Thinking Prompts
• What would you be looking for to
decide if two graphs were alike?
• Do any of the graphs go through the
same points?
•Do any of the graphs open in the same
direction?
• Are any of the graphs congruent to
other graphs?
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Scaffolding Thinking Prompts
Which one of the Scaffolding
Thinking Prompts do you like?
Why?
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Algebraic expressions
It takes more than 5 English
words to describe an algebraic
expression that has one term.
What could the algebraic and
verbal expressions be?
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Scaffolding Thinking Prompts
• How many English words does it
take to describe 2n?
• Could the algebraic expression
be 2n+3? Why or why not?
• How many terms would the
expression “a number squared”
take?
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Scaffolding Task:
Choose one of the open questions:
• Decide under what conditions you would
use those scaffolding questions.
This picture shows that 4x + 2 = 2 (2x + 1)
no matter what x is.
• Explain why.
• Now draw another picture that shows
another equation that is true no matter
what x is.
•Graph the 2 lines.
The 1st is 3x + 2y = 6 and
the 2nd is –x + 3y = 17.
A third line lies between them.
What might its equation be?
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General & specific scaffolds
•Most of the scaffolds we
just saw were very problem
specific.
• General scaffolds are also
helpful.
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Fail Safe Strategies
• Where have you seen
something like this before?
• What patterns do you see?
• Have you thought about….?
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General & specific scaffolds
http://www.edu.gov.on.ca
/eng/studentsuccess/lms
/files/tips4rm/TIPS4RMP
rocesses.pdf
•A useful source for
general scaffolds is
available in the
mathematical process
package in TIPS on
the Edugains website.
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Your turn to scaffold
•Looking at the
parallel task,
decide what
possible
scaffolds might
be needed.
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Thinking about feedback
• Suppose a student does well on a task. What
kind of feedback do teachers tend to give?
• Does that help the good student move on?
• Suppose a student does not do well on a task.
What kind of feedback do teachers tend to
give?
• Does that help the weak student to move on?
Looking at Student Work
• In pairs, pick one of the student’s work.
• What feedback would you give students
to move them forward?
• Share with another pair.
Assessment issues
•Open questions and parallel
tasks are built for instruction.
The focus is not on evaluation,
but…
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Assessment issues
•It makes total sense to use
parallel tasks to measure
communication and/or thinking
and maybe (depending)
knowledge or application.
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It is important …
•to use a previously shared
rubric or marking scheme
before posing such questions
to help students meet
success.
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Example 1
Task A:
• Think of a way to
represent the pattern
with the general term
3n +1.
• How does your
representation tell
you whether 925 is a
term in the pattern?
Task B:
• Think of a way to
represent a pattern
where each term
value is eight times
the term number.
• How does your
representation tell
you whether 925 is a
term in the pattern?
Learning goal: Represent the general term of a linear growing pattern
Possible Scoring Scheme
This could be marked as a 6-mark question
• 3 marks for a really good representation of the pattern which means
that you are representing the right pattern (which is the most important
thing) without errors
• 3 marks for a complete explanation for why 925 is or is not in
the pattern based on the representation
Another Example
Task A:
Explain and justify
each step you
would use in
solving the
equation without
using a calculator.
3
4 5
x 
2
3 3
Task B:
Explain and justify
each step you would
use in solving the
equation without
using a calculator.
1.5 x – 4.2 = 7.3
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Example 2
Task A:
Task B:
Sketch graphs
of y = 2x and
y = 2-x.
Sketch graphs
of y = x2 and
y = -2x2.
Tell how the graphs are
Tell how the graphs are
alike and different.
alike and different.
Which of those things could you have
predicted without sketching? Why?
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Possible Rubric
Learning Goal: Examine the effects of the parameters
given two graphs of the same type of function
Assessment issues
•It makes sense, even on a “test”,
to use open tasks to ensure that
students get an opportunity to tell
as much as they know in whatever
form works for them about an
idea they have learned.
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Example 3
Choose an equation to solve where the
solution is an integer. Solve it in at least
three different ways, explaining your thinking
for each method.
Suppose you had chosen an equation
where the solution turned out to be a fraction.
Which of your methods would be more
likely to help you? Why?
A possible Rubric
Learning Goal: Different representations of equations are
more useful depending on the situation.
Another Example
•Describe a number of examples
of measurements or situations
that would model direct
variation. What is it about them
that makes the variation direct?
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Another Example
•Give as many reasons as you
can to explain why there are
many quadratic relations that
pass through the points (0,0)
and (2,4).
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Assessment issues
•Although assessment of
learning should drive what
you teach, it should not limit
the strategies you use to
meet all students’ needs.
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Break out
Move to one of the following areas of
interest:
• Working with Student Samples
(Assessment for Learning)
• Developing Scaffolding Questions
• Forming Open & Parallel Questions
• Creating Consolidating Questions
Summarizing big ideas
•Our “big idea” for this PLMLC
series is that if you think more
broadly about what you are
focusing on in instruction, you
are more likely to:
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Summarizing big ideas
•help students make essential
connections
• ensure that students learn
what is really important
•ensure that a much broader
range of students can meet
success
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Work in Boards Group
• Talk about moving forward with the
ideas we have been working on
• Facilitators will be happy to join
your team if you want a different
set of eyes
• Call on another board to share ideas
Your questions
•You are welcome to ask any
questions or offer any insights on
what we’ve discussed in today’s
plenary .
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Next Steps – Professional Learning
• Sessions January to June 2010 with all
expenses paid by the ministry - possible
themes:
– K to Grade 8+ Mathematics Package
– Classroom Management Package
– Strategic planning work sessions
• Access customized provincial-level support
through Jeff Irvine, Myrna Ingalls, Demetra
Saldaris
• Regular postings on www.edugains.ca