Are you looking in the mirror or out the window?
Pausing Paraphrasing Probing for
specificity Putting ideas on
the table
Paying attention to self and others
Presuming positive intentions
Promoting a Spirit of Inquiry
Seven Norms of Collaboration
DuFour, Richard, et. al. Learning by Doing. Bloomington: Solution Tree, 2006. (p. 104)
PLT GOAL STATEMENTWhat can we do
differently in our leadership skills in order to
1) have powerful conversations with our PLT members and
2) grow in our capacity to lead the implementation of the CCRS, through the application of best practices?
Quality Instruction Scaffolding Professional Development Process
- Talk Moves- Conceptual Learning- Environment [physical & emotional]
- Productive Math Discussions- Task Selection- Quality Questioning
PLT 2012-2013
PLT 2013-2014
Classroom Impact
Type ofTraining
KnowledgeMastery
SkillAcquisition
ClassroomApplication
Theory 85% 15% 5-10%
PLUS
Practice 85% 80% 10-15%
PLUS
PeerCoachingStudy TeamsClass Visits
90% 90% 80-90%
Levels of Cognitive Demand
High LevelDoing MathematicsProcedures with Connections to Concepts,
Meaning and Understanding
Low LevelMemorizationProcedures without Connections to
Concepts, Meaning and Understanding
Hallmarks of “Procedures Without Connections” Tasks Are algorithmic Require limited cognitive effort for completion Have no connection to the concepts or meaning that
underlie the procedure being used Are focused on producing correct answers rather
than developing mathematical understanding Require no explanations or explanations that focus
solely on describing the procedure that was used
Procedures without Connection to
Concepts, Meaning, or Understanding
Convert the fraction to a decimal and percent38
3.008 .375 = 37.5%2 4
60
.375
564040
Hallmarks of “Procedures with Connections” Tasks
Suggested pathways have close connections to underlying concepts (vs. algorithms that are opaque with respect to underlying concepts)
Tasks often involve making connections among multiple representations as a way to develop meaning
Tasks require some degree of cognitive effort (cannot follow procedures mindlessly)
Students must engage with the concepts that underlie the procedures in order to successfully complete the task
“Procedures with Connections” Tasks
Using a 10 x 10 grid, identify the decimal and percent equivalent of 3/5.
EXPECTED RESPONSE
Fraction = 3/5
Decimal 60/100 = .60
Percent 60/100 = 60%
Hallmarks of “Doing Math” Tasks There is not a predictable, well-rehearsed pathway
explicitly suggested Requires students to explore, conjecture, and test Demands that students self monitor and regulated
their cognitive processes Requires that students access relevant knowledge
and make appropriate use of them Requires considerable cognitive effort and may
invoke anxiety on the part of students
Requires considerable skill on the part of the teacher to manage well.
“Doing Mathematics” Tasks
Shade 6 squares in a 4 x 10 rectangle. Using the rectangle, explain how to determine each of the following:
a) Percent of area that is shaded
b) Decimal part of area that is shaded
c) Fractional part of the area that is shaded
a) Since there are 10 columns, each column is 10% . So 4 squares = 10%. Two squares would be 5%. So the 6 shaded squares equal 10% plus 5% = 15%.
b) One column would be .10 since there are 10 columns. The second column has only 2 squares shaded so that would be one half of .10 which is .05. So the 6 shaded blocks equal .1 plus .05 which equals .15.
c) Six shaded squares out of 40 squares is 6/40 which reduces to 3/20.
ONE POSSIBLE RESPONSE
The Importance of Student Discussion
Provides opportunities for students to:
Share ideas and clarify understandings Develop convincing arguments regarding why
and how things work Develop a language for expressing
mathematical ideas Learn to see things for other people’s
perspective