Teaching to the Big Ideas

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Transcript Teaching to the Big Ideas

ERLC Presents…
A 12-Step Program for Student
Success in Mathematics
With Marian Small
A 12-step program
for student success
Marian Small
February 2010
Hello there
• Just so you know with whom you’re talking….
• Have a look-see!
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And so I know you…
• I’m curious as to what division you are in.
Could you let me know?
• A for Division 1
• B for Division 2.
• C for Division 3.
• D for Division 4.
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What led me here
• Teachers’ love of lists
• The existence of other “twelve step”
programs
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AA twelve steps
1. Admit life out of control
2. Admit greater power could restore you.
3. Decide to turn to a higher power.
4. Make a personal inventory.
5. Admit the problem to self and another.
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AA twelve steps
6. Be ready to remove defects.
7. Ask for help in removing shortcomings.
8. Be willing to make amends to those harmed.
9. Make the amends.
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AA twelve steps
10. Continue personal inventory and continue to
admit wrongs.
11. Prayer and meditation
12. Carry message to others.
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Our variation
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• Step 1: Recognizing a problem your students
might feel in your classroom
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What do you see as the
biggest problem?
A Not enough academic success
B Not enough confidence
C Not enough engagement
D Not enough joy
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• Step 2: Deciding you are the one to do
something about it
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A teacher’s role
• To your students, math is “you”- not a book,
not algebra, not numbers, not shapes.
• If things aren’t working, blaming lazy kids,
poor parenting, your principal, your
superintendent, your trustees, the Ministry or
the world gets you nowhere.
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• Step 3: Becoming self-aware without
condemning yourself
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Be kind
• We want students to honestly face their
learning struggles without making them feel
awful. We owe ourselves the same kindness.
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Think to yourself
• What do I do as a teacher that is really great?
Will somebody share here?
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Think to yourself
• Which kids seem not to connect with me? Why
might that be?
• Which colleagues seem not to connect with
me? Why might that be?
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Think to yourself
When colleagues seem not to connect with
me…. Is it because:
A I’m so good; they’re jealous
B I’m so bad that they don’t want the
association.
C We teach different grades or subjects.
D Our philosophical approaches are just too
different?
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• Step 4: Looking for a “sponsor”– working with
other teachers
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What makes us change?
• If our ideas are “confronted” either through
personal interactions or through reading.
• Where do we find our sponsor? It might be a
colleague, an administrator, a coach, a
consultant,…
Can someone share one experience where such
an interaction made them a better teacher?
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• Step 5: Gaining better insight into what and
how you are teaching by talking (to your
sponsor and others) and reflecting and/or by
reading and reflecting.
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Value of interaction
• We teach students about the value of working
in groups, teamwork, etc., so we need to
practise it.
• It’s about really hearing what someone else
does and why and being forced to tell
someone else what you do and why.
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• If you don’t have to talk to someone about
what you are doing, you often don’t notice
some of the things you’re not doing or realize
alternatives you could be doing.
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For example…
• You are teaching your students about
half/double, i.e. if you multiply two numbers,
you can halve one and double the other (e.g.
18 x 25 = 9 x 50)
• You say it works since you are doing the
opposite to each number.
• I (a colleague) come along and ask….
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• So how come that doesn’t work for division?
(Why isn’t 300 ÷ 50 = 600 ÷ 25?)
• It is only then that you realize that there were
some glaring omissions in what you had told
your students.
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Would you:
A
Just clarify by saying it only works for x
B
Explain why it only works for x using
examples
C
Explain why it only works for x using
reasoning
D Ask kids to figure out why it only works for x?
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8x6
xxxxxx
xxxxxx
xxxxxx
xxxxxx
xxxxxx
xxxxxx
xxxxxx
xxxxxx
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8÷2
xx
xx
xx
xx
4÷4
xxxx
Not enough stuff and too many
sharers
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Or…
• You are teaching students how to solve
proportions. Lots of students struggle when
solving a proportion such as 4/x = 3.2/80.
• You talk to another teacher to get an idea, e.g.
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Ratio table
3.2
80
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800
8
200
4
100
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Or…
• You are teaching students how to calculate
the mean of 58, 57, 55, 70 and 68.
• You never realized, until you talked to
someone else, you could think of each number
in terms of 60, so it’s really the mean of:
60 – 2, 60 – 3, 60 – 5, 60 + 10 and 60 + 8, so
you could calculate the mean of -2, -3, -5, +10
and +8 and just add 60.
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• In addition, a conversation with other
teachers can help you clarify what your
learning goals can or should be, different
pedagogical approaches you could take, or
missed opportunities.
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What to read?
• Our math teaching benefits by reading math-
specific material. Whether they are books and
articles that give us more insight into the
math content we teach or pedagogical
approaches ….
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What to read?
• Whether they are books and articles that are
research based or that are personal
reflections….
• Whether they are in print or on the internet….
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• Step 6: Teaching through problem solving
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What does it mean?
• You don’t teach a whole bunch of techniques
so that kids can solve “problems” of a certain
type. (They aren’t problems if the kid knows
the type they are anyway.)
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What does it mean?
• Instead you present the problem and let kids
try. The problems are not random; you make a
professional judgment about where your
students need to and can go.
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What does it look like?
• In Grade 4, I might ask my students
something like:
• I used 43 sticks to make triangles, squares
and hexagons. What did I make?
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What does it look like?
43 sticks to make triangles, squares and
hexagons.
Choose which answer might be reasonable:
A: all triangles
B: all squares
C: 5 hexagons and some squares
D: 3 hexagons and some squares and triangles
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What does it look like?
• Or, more specifically….
• A) How many of each shape might I have
made?
• B) How do you know that at least one shape
was a triangle?
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What does it look like?
• In Grade 6, I might ask my students
something like: A parallelogram has an area
of 32 cm2. What might its dimensions be?
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What should I ask now?
A: Could the parallelogram be really long?
B: Could the height be 4?
C: Could the height be just a little less than the
base length?
D: What do you know about the parallelogram?
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What should I ask now?
A: Could the parallelogram be really long?
B: Could the height be 4?
C: Could the height be just a little less than the
base length?
D: What do you know about the parallelogram?
Someone explain their choice.
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What does it look like?
• In Grade 9, I might ask my students
something like: Without using a protractor,
how do you know that these line segments on
a geoboard are perpendicular?
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What does it look like?
• Look at the rises and runs.
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• Step 7: Planning ahead what to ask and, as
much as possible, how to respond, but with a
willingness to change.
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Planning questions
• When you write a lesson plan, you could be
thinking about the questions you should ask
that bring out the big idea and that ensure
that all students’ needs are addressed.
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For example…
• You are teaching a grade 4 lesson on dividing
two-digit numbers by one-digit numbers, e.g.
78 by 6.
• What do you think are the one or two most
important ideas you want students to walk
away with?
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Is it…
A That division describes the equal groups when
you divide up a whole.
B That you can accomplish division by thinking
about subtraction or multiplication.
C That you should estimate before you
calculate
D The procedure for dividing
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So what might you ask..
• Describe a situation where you might divide
50 by 4.
• Now describe a situation where you are
forming groups but you would not divide.
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Or…
• Jennifer said that you can’t divide 50 by 4
since if you try to make equal groups it
doesn’t work. What would you say to Jennifer?
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Or…
• Tell how dividing is related to multiplying.
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Or…
• Alicia says that 45 – 9 – 9 – 9 – 9 – 9 = 0
describes a division. Do you agree? Explain.
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Grade 8 example
• You are teaching students to solve linear
equations with integer solutions, using a
variety of strategies (e.g. 2n + 1 = 17).
• What are the most important things you want
students to know?
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Maybe…
• That an equation is a statement of balance.
• That the equation has many “equivalent”
forms, e.g. 2n + 1 = 17 is equivalent to 2n = 16
or 2n + 2 = 18 or….
• That solving an equation is finding the
“simplest” equivalent form.
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So you could plan to ask…
• Which of these equations do you think are
most alike? Why do you think that?
3n - 1 = 17
36 – 6n = 0
3n – 4 = 20
18 – n = 2n
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Or…
• Give three equations equivalent to (with
exactly the same solutions as) 10 – n = 6.
• Kylie said that if 8 + 4 = x + 5, then x = 12. Do
you agree? Explain why you agree or
disagree.
• Lenee said that 5 + n = 12 is just the equation
n = 7 “in disguise”. Do you agree? Explain why
you agree or disagree.
Which did you like best? Can someone share?
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• Step 8: Recognizing that different students
need different “treatment.”
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Recognizing differences
• recognizing student talents and interests.
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Recognizing differences
• You could provide choice in consolidation (or
practice) or choice in instruction.
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Recognizing differences
• For example, if you have students who really
like to “debate”, then include as one of the
assignment choices the opportunity to debate.
A student could take the pro or con side on
“You never really need to learn how to divide
if you know how to multiply.”.
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Recognizing differences
• In an instructional situation, you could provide
alternate activities for students who need
those alternatives.
• For example, if you wanted lots of students to
multiply two 2-digit numbers, but some are
really not ready, you could provide these
alternatives.
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Multiplication
Task 1:
Task 2:
• A hotel has 24
• A hotel has 24
windows on a
floor. There are
19 floors. How
many windows
are there?
windows on a
floor. There are 9
floors. How many
windows are
there?
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Some common questions
• Is the number of windows more than 240?
How do you know?
•
How would you estimate the number of
windows?
• How could you use manipulatives or a diagram
to model the problem?
• How could you use mental math to solve the
problem?
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Or…
• Or you could ask more open-ended questions.
For example, in grade 3, when working on
addition of 3-digit numbers, you could say:
• Create an addition problem where you add a
number greater than 30 to 38. Solve your
problem.
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Too many …
• teachers believe that whatever way they think
is clearest is clearest to everyone.
• parents believe that whatever way they
remember is the right way.
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• Step 9: Responding to individual students.
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Ensuring praise
• Every child needs genuine praise.
• You need to be assigning tasks where
students can succeed so you can praise.
• Praise works best when the tasks allow for
unique responses.
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Giving feedback
• The best feedback you can give is personal; it
picks up specifically on what the student has
said.
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Giving feedback
• Suppose a Grade 1 student says that 15 – 8 is
less than 15 – 10 since 8 is less than 10.
Will someone share?
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Giving feedback
• Suppose a Grade 5 student says that 6/4 is not
a fraction since fractions are parts of wholes
and that isn’t. What would you say?
Can someone share?
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Giving feedback
• Suppose a Grade 9 student says that
-4 - (-3)
= 7 since two negatives make a positive. What
would you say?
Can someone share?
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• Step 10: Making what you teach your own.
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Too many teachers..
• tell me that they are asking a question that
makes no sense to them just because it’s in
the book.
• What you do has to make sense to you.
Ultimately you are responsible for the
instruction in the class– if the students don’t
see you comfortable, it’s very unlikely they
can be.
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• Step 11: Relaxing
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Uptight is bad.
• Too many teachers are “obsessed” with
wording, with following instructions that are
peripheral,….
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For example…
• You ask students to pace off the length of the
classroom. One student does the width
instead.
• Who cares?
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Uptight is bad.
• If we could relax a bit and go with the flow,
classrooms would be more pleasant
environments, students would take more
risks, and there would be much less stress all
around.
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• Step 12: Staying the course and carrying the
message if you’re up for it.
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Persistence
• Persistence is the key.
• You have to try.
• You have to try more than once.
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Taking initiative
• You can be the leader as well as a follower
and encourage others.
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So….
• If you want a checklist,…
• If not, there is a bigger picture here. I actually
think that the three big issues I’ve addressed
are the need to take responsibility for your
instruction, the need to work
collaboratively, and the need to really think
hard about what you do.
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Teaching is…
• constantly staying up to date,
•
conferring and talking over “cases”, and
• considering the individual welfare of each of
our “patients/clients”
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Thank You
• You can download this presentation on my
website:
www.onetwoinfinity.ca
Look for: West Webinar
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