Transcript CGI Experimental Study - Teachers Development Group

Knowledge of Children's
Mathematics: A Foundation for
Classroom Discourse
Perspectives from Cognitively
Guided Instruction.
Linda Levi
Linda Levi, TDG Seminar, 2-2006
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Summary of Major Cognitively
Guided Instruction (CGI) Research
Thomas Carpenter, Megan Franke, Elizabeth Fennema,
Penelope Peterson, Linda Levi, Victoria Jacobs,
Susan Empson and others.
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1970s Research on Children’s Thinking
1984-88: CGI Experimental Study
1989-95: CGI Longitudinal Study
1996-05: CGI/Algebra Development and
Research
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1970s: Research on Children’s
Mathematical Thinking
• Thomas Carpenter and James Moser
research the development of children’s
strategies for addition and subtraction
problems
Linda Levi, TDG Seminar, 2-2006
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1984 - 1988: CGI Experimental Study
• First grade teachers
– 20 participated in CGI professional development
(summer workshop)
– 20 participated in general problem solving workshop
• Treatment and Control group were compared
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Teachers’ knowledge
Teachers beliefs
Students’ achievement (problem solving and facts)
Classroom practice (amount of problem solving, type
of teacher talk, type of student talk…)
Linda Levi, TDG Seminar, 2-2006
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1989-1995:CGI Longitudinal Study
• Kindergarten through third grade teachers and
students in four schools
• All teachers attended CGI professional
development
• The following were assessed over three years:
– Teachers’ knowledge and beliefs
– Students’ achievement and beliefs
– Classroom practice
• A study of these teachers’ classroom practice,
knowledge and beliefs was done five years after
the workshop ended.
Linda Levi, TDG Seminar, 2-2006
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1996-2005: CGI/Algebra Research
• 1996 – 2000 CGI Algebra Professional Development
Program was developed by researchers in conjunction
with expert CGI teachers.
• 2000 -05 Experimental Research
– 90 Kindergarten – Sixth grade teachers attended
CGI/Algebra professional development
– These teachers were compared with 90 teachers who
did not attend
• Student Achievement
• Teacher Knowledge
Linda Levi, TDG Seminar, 2-2006
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Cognitively Guided Instruction
Summary of Major Research Results
• CGI Students’ achievement on problem solving tasks is
higher than non-CGI students’.
• CGI Students’ performance on computation and facts is
not significantly different from that of non-CGI students.
• CGI Teachers have greater knowledge of their own
students’ thinking than non-CGI teachers.
• CGI Teachers have greater knowledge of children’s
mathematics than non-CGI teachers.
• CGI Classrooms involve a great deal of problem solving
and student discussion.
• Most Teachers sustain their practice 5 years after PD
ends.
• Some Teachers generated additional growth 5 years
after PS ended.
Linda Levi, TDG Seminar, 2-2006
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Outcomes of Classroom Discourse
Discourse
Students learn
from students
Students’
reflect on
their own
ideas
Teachers learn
about
Children’s
mathematics
Teachers
learn about
their
students’
thinking
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“I always knew it was important to
listen to kids, but I didn’t know
what to listen for.”
CGI teacher, 1989
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Foundation for Discourse:
• Teacher’s Knowledge of Children’s
Mathematics
• Teacher’s Knowledge of his/her
individual students’ thinking.
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Rachel’s Problems
• Rodney is having some kids over for jelly
donuts. 7 donuts can fit on one plate. How
many plates will Rodney need for 28 donuts?
• Karina had 20 cupcakes. She put them into 4
boxes so that there were the same number of
cupcakes in each box. How many cupcakes did
Karina put in each box?
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Multiplication, Measurement Division and Partitive
Division Problems
• Multiplication
Susan has 8 boxes with 5 marbles in each bucket. How
many marbles does Susan have?
• Measurement Division
Susan has 40 marbles. She wants to put them into
boxes with 5 marbles in each box. How many boxes
would she need to hold all of her marbles?
• Partitive Division
Susan has 40 marbles. She has 5 boxes to hold these
marbles. How many marbles can she put in each box if
she wants to put the same number of marbles in each
box?
Linda Levi, TDG Seminar, 2-2006
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Problems to classify:
1. I have 21 cents to buy candies with. If each
gum drop costs 3 cents, how many gum drops
can I buy?
2. Janelle has 21 beads. She wants to make 3
braids in her hair and put the same number of
beads in each braid. How many beads can go
in each braid?
3. Kevin earned 89 bonus points when playing his
computer game. If it takes 7 bonus points to
get an extra life, how many extra lives will he
get?
Linda Levi, TDG Seminar, 2-2006
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Multiplication Problems
1. There are 2 bags of soccer balls with 10 balls in each
bag. There are also 4 extra balls. How many balls are
there altogether?
2. Mia has 7 bags of beads. There are 10 beads in each
bag. She also has 6 extra beads. How many beads
does she have?
3. Ms. Keith has 6 packages of cookies. There are 10
cookies in each package. She also has 4 other
cookies. How many cookies does she have?
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Measurement Division Problems
1. Matt has 36 pennies. He puts 10 pennies into each
box. How many boxes can he fill with 10 pennies?
2. David has a rock collection. He has 54 rocks in his
collection. He puts them into boxes with 10 rocks in
each box. How many boxes does he use?
3. The second graders had 54 balloons for the school
carnival. They put balloons into bunches of ten. How
many bunches could they make?
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Strategies for Solving Multiplication and
Measurement Division Problems with Tens
• Counting by Ones
• Counting by Tens
• Direct Place Value
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•
Sam eats 1/10 of a pound of fudge a
day. How many days would it take him to
eat 2 pounds of fudge?
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• An animal at the zoo eats .1 of a pound of
food each day. If the zookeeper has 65.4
pounds of food for this animal, how many
days can she feed the animal before the
food runs out?
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• How many tens are in 387? How many
tenths are in 387?
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• In the early 1900’s, a farmer could pile up
stones to construct .1 of a mile of fence a
day. If a farmer worked for 35 days
building a fence, how long would the fence
be?
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• Sam builds .35 mile of fence every day.
How long would his fence be after 32
days?
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