Transcript PK-5 Math Forum

PK-5 MATH FORUM
October 4, 2012
I need exactly 4 quarts of water to make a
punch for the class party. I have a 5 qt.
bucket and a 3 qt. bucket. How can I
measure exactly 4 qt. of water using just
these two buckets?
How would you model this problem
to help you think it through?
How would you record your steps to
communicate what you did?
How many different solutions?
http://e2math.weebly.com/
• Explain “why”
• Important Updates
• Models to Support Thinking
• Promote collaboration and communication
• Blog format
• Support your work as teacher leaders in your districts
• PK-5 Implementation
• PK-5 Forum
http://parcconline.org/samples/item-task-prototypes
Advances in the PARCC
Mathematics Assessment
August 2012
4
PARCC’s Fundamental Advance
PARCC is designed to reward quality
instruction aligned to the Standards, so the
assessment is worthy of preparation rather
than a distraction from good work.
5
PARCC’s Core Commitments to
Mathematics Assessment Quality
6

Focus: PARCC assessments will focus strongly on where the Standards
focus. Students will have more time to master concepts at a deeper
level.

Problems worth doing: Multi-step problems, conceptual questions,
applications, and substantial procedures will be common, as in an
excellent classroom.

Better Standards Demand Better Questions: Instead of reusing existing
items, PARCC will develop custom items to the Standards.

Fidelity to the Standards (now in Teacher’s hands): PARCC evidences are
rooted in the language of the Standards so that expectations remain the
same in both instructional and assessment settings.
What is Different About PARCC’s
Development Process?
 PARCC states first developed the Model Content Frameworks to
provide guidance to key elements of excellent instruction aligned
with the Standards.
 The Model Content Frameworks were then used to provide
guidance in the content emphasis for the mathematics
assessment.
So, for the first time. . .
 PARCC is communicating in the same voice to teachers as it is to
assessment developers!
 PARCC is designing the assessments around exactly the same
SHIFTS the standards expect of teachers and students.
7
What Are the Shifts in the Math
Standards at the Heart of PARCC Design?
1. Focus: The PARCC Assessment will focus strongly
where the Standards focus
2. Coherence: Think across grades and link to major
topics within grades
3. Rigor: In major topics, pursue conceptual
understanding, procedural skill and fluency, and
application.
8
Advances in Assessment
Specific advances in the PARCC mathematics
assessments demanded by the three shifts…
9
Advances in Assessment Demanded by
the Shifts
Shift #1 – Focus: The PARCC assessments will focus
strongly where the Standards focus
Advance: PARCC assessments will focus strongly
where the Standards focus (70% or more on the
major work in grades 3-8).
 Focus allows for a variety of problem types to get at
concept in multiple ways.
 Students will have more time to master concepts at a
deeper level.
10
Advances in Assessment Demanded by
the Shifts
Shift #2 - Coherence: Think across grades, and link to
major topics within grades
Advance: The assessment design is informed by
multi-grade progressions in the Standards and the
Model Content Frameworks.
 Key beginnings are stressed (e.g., ratio concepts in grade
6), as are key endpoints and takeaway skills (e.g., fluency
with the multiplication table in grade 3).
11
Advances in Assessment Demanded by
the Shifts
Shift #2 - Coherence: Think across grades, and link to
major topics within grades
Advance: Integrative tasks draw on multiple
standards to ensure students are making important
connections.
 The Standards are not treated as a checklist.
12
Advances in assessment demanded by
the shifts
Shift #3 - Rigor: In major topics, pursue conceptual
understanding, procedural skill and fluency, and
application
Advance: PARCC assessments will reach the rigor in
the Standards through innovations in technology and
item design…
13
Using Technology to Advance
Assessment and the Shifts
•
•
•
14
Technology enhancements supporting accessibility
(e.g., the ability to hover over a word to see and/or
hear its definition, etc.)
Transformative formats making possible what can
not be done with traditional paper-pencil
assessments (e.g., simulations to improve a model,
game-like environments, drawing/constructing
diagrams or visual models, etc.)
Getting beyond the bubble and avoiding drawbacks
of traditional selected response such as guessing or
choice elimination.
Using Technology to Advance
Assessment and the Shifts
•
•
15
Capturing complex student responses through a
device interface (e.g., using drawing tools, symbol
palettes, etc.)
Machine scorable multi-step tasks are more
efficient to administer and score.
Sample Items Illustrating the Advances in
Assessment
The next section of this presentation is comprised of
sample items that illustrate some of the advances called
for by the three shifts.
16
Overview of Mathematics Task Types
PARCC mathematics assessments will include three types of tasks.
Task Type
Description of Task Type
I. Tasks assessing
concepts, skills and
procedures
•
•
•
•
Balance of conceptual understanding, fluency, and application
Can involve any or all mathematical practice standards
Machine scorable including innovative, computer-based formats
Will appear on the End of Year and Performance Based Assessment
components
II. Tasks assessing
expressing
mathematical
reasoning
•
Each task calls for written arguments / justifications, critique of
reasoning, or precision in mathematical statements (MP.3, 6).
Can involve other mathematical practice standards
May include a mix of machine scored and hand scored responses
Included on the Performance Based Assessment component
III. Tasks assessing
modeling /
applications
•
17
•
•
•
•
•
•
Each task calls for modeling/application in a real-world context or
scenario (MP.4)
Can involve other mathematical practice standards.
May include a mix of machine scored and hand scored responses
Included on the Performance Based Assessment component
For more information see PARCC Item Development ITN Appendix D.
18
FLUENCY
To support mathematical thinking
Erin Wheeler, IES Erie 2 BOCES, 8-26-2012
Counting Fluency
PK- K
1-2
1-3
1’s
(pennies)
1-5
5’s
(nickels)
1-10
10’s (dimes)
Up to 100
23, 33, 43, etc.
“math way”
1 ten 2, 1 ten
3,
Up to 120
Whisper/
speak
Roller coaster
Whisper odd,
speak evens
Repeated + or
subtraction
3
4-5
Multiples of
Multiples of
whole numbers unit fractions/
whole numbers
Unit fractions
(beyond 1Decimals
keep as
improper
fractions)
Erin Wheeler, IES Erie 2 BOCES, 8-26-2012
Sprints
Bill Davidson
http://www.youtube.com/watch?v=G_y9gGnd68M
Erin Wheeler, IES Erie 2 BOCES, 8-26-2012
Application
Problem solving requires students
to apply the 8 Mathematical Practices
Bill McCallum – “Structuring the Mathematical Practices”
http://commoncoretools.me
Erin Wheeler, IES Erie 2 BOCES, 8-26-2012
Table I and 2
Making the Connection
9 + 6 = 15
Abstract
Pictorial
Concrete
Erin Wheeler, IES Erie 2 BOCES, 8-262012
Multipurpose Models
• Number path
• Number stairs
• Number bond
• Place Value Models
• Ten frames, bundles, base ten blocks, money, number disks
• Bar Model
• Area Model
• Number line
• Array
• Rekenrek- physical model of an array
Erin Wheeler, IES Erie 2 BOCES, 8-262012
Second Grade
8 children are swimming in the pool. 5 more
children jump in. How many children are in the pool
now?
?





8 children
8 + 5 = 13








5 more
13 children are in the pool.
Erin Wheeler, IES Erie 2 BOCES, 8-262012
Marcus has 12 pencils. Sergio has 3
more pencils than Marcus. How
many pencils does Sergio have?
Erin Wheeler, IES Erie 2 BOCES, 8-262012
Jerry has 12 eggs. He gave 3 to
Kevin. How many eggs does Jerry
have now?
Erin Wheeler, IES Erie 2 BOCES, 8-262012