Professional Practice Norms
 Listening to and using others’ ideas
 Keeping records of professional work
 Adopting a tentative stance toward
practice - wondering versus certainty
 Backing up claims with evidence and
providing reasoning
 Talking with respect yet engaging in
critical analysis of teachers and students
portrayed
Seago & Mumme, 2003
1
Math & Science Collaborative at
the Allegheny Intermediate
Do the Math
Shade six of the small squares in the rectangle shown below.
Using the diagram, explain how to determine:
a) the percent of area that is shaded
b) the decimal part of area that is shaded
c) the fractional part of the area that is shaded
Math & Science Collaborative
The Case of Ron Castleman
Read the case from page 36 through 42
where it is clearly marked “STOP.”
Math & Science Collaborative
The Case of Ron Castleman
Following the second period class:
1. What are some mathematical issues Ron was concerned
with during the lesson? Why are these important issues?
What non-mathematical issues did Ron seem to be
concerned about?
2. How would you describe the thinking Ron was asking
students to engage in when he set up the task? Did
Ron’s goals change after the students began working on
the task? Were Ron’s goals accomplished?
Math & Science Collaborative
The Case of Ron Castleman
Read the remainder of the case through page 46.
Math & Science Collaborative
The Case of Ron Castleman
Following the sixth period class:
3. How would you describe the thinking Ron was asking
students to engage in when he set up the task for his
sixth period class?
a) Did Ron seem to have the same initial goals for both
classes?
b) Did the students in the sixth period class engage with
the task in the same way as those in the second
period class? What was learned in each class?
Math & Science Collaborative
Linking to Literature/ Research:
The QUASAR Project
The Math Task Framework
TASKS
TASKS
as they
appear in
curricular/
instructional
materials
as set up by
the teachers
TASKS
as
implemented
by students
Math & Science Collaborative
Student
Learning
Cognitive Demands at Set Up
N
T
IZ
A
IT
M
E
M
O
R
C.
W
O
PR
E
U
R
D
CE
PR
O
IO
H
O
U
W
IT
H
S
M
AT
H
G
IN
O
D
T
45
40
35
30
25
20
15
10
5
0
Stein, Grover, & Henningsen, 1996
Math & Science Collaborative
The Fate of Tasks Set Up as
Doing Mathematics
10%
Doing Mathematics
14%
Unsystematic
Exploration
No Mathematics
37%
Procedures
WITHOUT
Other
17%
22%
Stein, Grover, & Henningsen, 1996
Math & Science Collaborative
The Fate of Tasks Set Up as
Procedures WITH Connections to Meaning
2%
2%
Procedures
WITHOUT
Procedures WITH
43%
53%
Memorization
No Mathematics
Stein, Grover, & Henningsen, 1996
Math & Science Collaborative
Patterns of Implementation
 In a 3-year study of classroom instruction
at four QUASAR middle schools, a handful
of patterns emerged that captured
characteristic ways in which high level tasks
unfolded during instruction.
 We will look at the patterns and the
classroom-based factors associated these
patterns.
Math & Science Collaborative
Factors Associated with the Maintenance and
Decline of High-Level Cognitive Demands






Routinizing problematic aspects of
the task
Shifting the emphasis from meaning,
concepts, or understanding to the
correctness or completeness of the
answer
Providing insufficient time to wrestle
with the demanding aspects of the
task or so much time that students
drift into off-task behavior
Engaging in high-level cognitive
activities is prevented due to
classroom management problems
Selecting a task that is inappropriate
for a given group of students
Failing to hold students accountable
for high-level products or processes
Stein, Grover & Henningsen, 1996
Math & Science Collaborative
Factors Associated with the Maintenance and
Decline of High-Level Cognitive Demands







Scaffolding of student thinking and
reasoning
Providing a means by which
students can monitor their own
progress
Modeling of high-level
performance by teacher or capable
students
Pressing for justifications,
explanations, and/or meaning
through questioning, comments,
and/or feedback
Selecting tasks that build on
students’ prior knowledge
Drawing frequent conceptual
connections
Providing sufficient time to explore
Math & Science Collaborative
Factors Associated with the Maintenance and
Decline of High-Level Cognitive Demands
Decline






Maintenance
Routinizing problematic aspects of
the task
Shifting the emphasis from meaning,
concepts, or understanding to the
correctness or completeness of the
answer
Providing insufficient time to wrestle
with the demanding aspects of the
task or so much time that students
drift into off-task behavior
Engaging in high-level cognitive
activities is prevented due to
classroom management problems
Selecting a task that is inappropriate
for a given group of students
Failing to hold students accountable
for high-level products or processes







Scaffolding of student thinking and
reasoning
Providing a means by which
students can monitor their own
progress
Modeling of high-level
performance by teacher or capable
students
Pressing for justifications,
explanations, and/or meaning
through questioning, comments,
and/or feedback
Selecting tasks that build on
students’ prior knowledge
Drawing frequent conceptual
connections
Providing sufficient time to explore
Math & Science Collaborative
The Case of Ron Castleman
Following the sixth period class:
What classroom-based factors might have contributed to
the different kinds of student engagement in the two
classes?
a) What did Ron do differently in the two classes that might have
supported (or not supported) students’ engaging in the task as
he intended? What, if anything, did he do that was the same?
b) What did the students do in each class that might have
influenced their own learning and engagement with the task?
Math & Science Collaborative
Does Maintaining
Cognitive Demand Matter?
YES!!
Math & Science Collaborative
Research shows . . .
That maintaining the cognitive
complexity of instructional tasks
through the task enactment phase is
associated with higher student
achievement.
Math & Science Collaborative
Assessing Student Learning
Task & Set-Up
Learning
Implementation
Student
High
Level
High
Level
Significant
Gains
High
Level
Low
Level
Moderate
Gains
Low
Level
Lowest Gains
Low
Level
Math & Science Collaborative
The Case of Ron Castleman
What can we learn about the
teaching and learning of
mathematics from this case?
Math & Science Collaborative
Link to SAS
 How do you see the Math
Task Framework linking to
the Standards Aligned
System?
TASKS
TASKS
TASKS
as they
appear in
curricular/
instructional
materials
as set up by
the teachers
as
implemented
by students
Student
Learning
Math & Science Collaborative
Individual Reflection
 Identify one pedagogical move used
by Ron Castleman which is not
currently part of your own
pedagogical practice. Why was this
an important move for Ron Castleman
and why might it be worth
considering this strategy in your
practice?
Math & Science Collaborative
Looking Back Across the
Pedagogical Moves
 Review the transcripts and lesson graphs
from the first two VCMPD sessions
 Determine what factors were at play in
each classroom which either maintained
the high level cognitive demands of the
task or contributed to their decline (refer
to page 16 in the purple book)
 Be certain to cite evidence (time in the
transcript or lesson graph)
Math & Science Collaborative
This material is based on work supported by the
National Science Foundation under Grant No. EHR0314914. Any opinions, findings, conclusions, or
recommendations expressed in this publication are
those of the authors and do not necessarily reflect the
views of the granting agency.
23
Math & Science Collaborative at
the Allegheny Intermediate