A Series of Four CIVS
Instructional Facilitators, Math Content Leads,
Specialists and Administrators
December 1, 2011
February 29, 2012
May 16, 2012
Questions
Collect at your site
Send as an e-mail
Aimee.evans@archford.org or
aimee.evans@sbcglobal.net
Deadline 12:30 pm
AR Frameworks vs. CCSS
Witten by Arkansas Teachers for Arkansas
Teachers
A National Working Group and a Three Person
Writing Team
http://www.youtube.com/user/TheHuntInstitute p/u/dnjbwjdcPjE
Progressions
Content Progression
Learning Progression
Learning Trajectories
Construct Maps
Content Progressions
…narrative documents describing the
progression of a topic across a number of grade
levels, informed both by research on children's
cognitive development and by the logical
structure of mathematics.
http://ime.math.arizona.edu/progressions/
Learning Progressions
Four Interrelated Guiding Principles of Learning Progressions (LPs)
1.
LPs are developed (and refined) using available research and evidence
2.
LPs have clear binding threads that articulate the essential core concepts
and processes of a discipline (sometimes called the ‘big ideas’ of the
discipline)
3.
LPs articulate movement toward increased understanding (meaning deeper,
broader, more sophisticated understanding)
4.
LPs go hand-in-hand with well-designed and aligned assessments
http://www.nciea.org/publications/Math_LPF_KH11.pdf
Learning Trajectories
If it can be established that most students, at least within a particular
society, within a wide range of ability, and with access to
appropriate instruction, follow a similar sequence, or even a small
finite range of sequences, of levels of learning of key concepts and
skills, then it should be possible not only to devise instructional
sequences to guide students in the desired directions, but it should
also be possible to develop standards and expectations for students’
performance that are referenced to those sequences; so that the
standards, and derived assessments, report in terms that have
educational meaning and relevance.
http://www.cpre.org/ccii/images/stories/ccii_pdfs/learning%20trajectori
es%20in%20math_ccii%20report.pdf
Construct Maps
describe how children come to understand
Richard Lehrer - Vanderbilt
Standards and Curriculum
Standard is the goal.
Curriculum is a plan for achieving the goal.
Relationship
Standards drive curriculum.
Curriculum leads to meeting standards.
Example 1
2.MD.8 Solve word problems involving dollar
bills, quarters, dimes, nickels and pennies, using
$ and ¢ symbols appropriately.
This does not give the learning progression
(learning trajectory/construct map) necessary to
achieve this goal.
Example 2
No where in the CCSS is there a standard about
divisibility rules but these rules might be a part of a
learning trajectory leading to a standard like:
4.NF.1 Explain why a fraction a/b is equivalent to a
fraction (n × a)/(n × b)….
7.NS.2d Convert a rational number to a decimal using
long division, know that a rational number
terminates in 0s or eventually repeats.
Learning Progressions
Formative Assessment
Formative assessments should be designed to
help teachers identify where a student is in a
learning progression, indicating the next steps
for instruction with each student and or “group”
of students. (RTI)
We must attend to each students cognition
(thinking) at each step in the instructional
sequence.