Post on 02-Jan-2016
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Our Learning Journey
ContinuesShelly R. Rider
College and Career-Ready Standards for Mathematics
The Practice Standards and Content Standards define what students should understand and
be able to do in their study of mathematics. Asking a student to understand something
Means asking a teacher to assess whether the student has understood it. But what does
Mathematical understanding look like? One hallmark of mathematical understanding is the
ability to justify, in a way appropriate to the student’s mathematical maturity, why a
particular mathematical statement is true or where a mathematical rule comes from. There
is a world of difference between a student who can summon a mnemonic device to expand
a product such as (a + b)(x + y) and a student who can explain where the mnemonic comes
from. The student who can explain the rule understands the mathematics, and may have a
better chance to succeed at a less familiar task such as expanding (a + b + c)(x + y).
Mathematical understanding and procedural skill are equally important, and both are
assessable using mathematical tasks of sufficient richness.
Mathematical Understanding
The Overarching Habits of Mindof a Productive Mathematical Thinker
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
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
Quality Instruction Scaffolding Professional Development Process
- Talk Moves- Conceptual Learning- Environment [physical & emotional]
Grade Level Teachers 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%
PLT TEAMS
Peer to Peer Coaching
Peer to Peer Coaching is a confidential process through which two or
more professional colleagues work together
to reflect on current practices.
Immediate Next Steps of the CCRS Journey1) Peer-to-Peer Coaching
Process
2) Vertical Math PLT Process
Talk Move PD August Part 1
Talk Move Facilitator Notes to guide the PD
Talk Move Participant PacketTalk Move PowerPointTalk Move Video(s)Talk Move Research Article
These resources will be located at http://amsti-usa.wikispaces.com at the close of Monday, August 5th.
The Journey Ahead Form
&Peer-to-Peer
Coaching Form
PD Structures to Facilitate Learning
Teacher Professional Learning Teams PLT Facilitator Coaching Communities PLT Facilitator Side-by-Side Coaching Administrator Professional Learning
Teams Peer-to-Peer Coaching
Our Learning Journey
ContinuesShelly R. Rider