FAIRFAX COUNTY PUBLIC SCHOOLS
APRIL 2013
WHAT STUDENTS KNOW AND CAN DO
OECD Test for Schools (based on PISA)--Mathematics
Assessment Items
The Three Dimensions of Mathematics
• Content- overarching ideas in relation to strands
– Overarching ideas-patterns in space and shape,
patterns in change and relationships, patterns in
quantity, uncertainty
– Strands- numbers, algebra and geometry
• Process- general mathematical competencies
– Reproduction- computations or definitions
– Connections- connections to be made to solve
relatively straightforward problems
– Reflection- mathematical thinking,
generalization and insight
• Situation- personal, educational or
occupational, public and scientific.
Conditions and Format
• Every task is in context of a real life situation
• Many tasks have multiple parts
• Combination of multiple choice and constructed response
– Multiple Choice 14
– Constructed Response 26
• Opportunities to explain process or justify answer
• Paper-pencil test
• Calculators and other tools as they are normally
used in school
• No accommodations provided
• 2 hours total for the entire test
• Partial credit awarded
Difficulty score of 406
Difficulty score of 439
Difficulty score of 586
Comparing VA SOL Questions and
PISA Sample Tasks
2001 Geometry Standards
A company makes two similar cylindrical
containers. The total surface area of the
small container is 0.81 times that of the
larger container. The height of the larger
container is 60 cm. What is the height of the
smaller container?
A.
B.
C.
D.
54 cm
48.6 cm
24.3 cm
21 cm
2009 Geometry Standards
Comparing Questions
Performance Data
Tear Share Overview
Look Over the Artifacts
Tear-Share Debrief
Each Number Group Shares
Adapted from Supporting Differentiated Learning Solution Tree 2011
Look at the Mathematics Artifacts
Part 1: 7 minutes
 Explore the 4 artifacts related to
the mathematics data
 Take notes on your graphic
organizer while working.
Adapted from Supporting Differentiated Learning Solution Tree 2011
Debrief
Part 2: 7 minutes
• Number off from 1 – 4.
• Tear and share your box sections:
–
–
–
–
All of the 1’s go to person 1
All of the 2’s go to person 2
All of the 3’s go to person 3
All of the 4’s go to person 4
Adapted from Supporting Differentiated Learning Solution Tree 2011
Sharing
Part 3: 5 minutes
Number groups summarize the responses
in their boxes and prepare to share.
Adapted from Supporting Differentiated Learning Solution Tree 2011
Artifact #1 Levels of Mathematics Performance
Level
Condensed Description
6
•capable of advanced mathematical thinking and reasoning
•precisely communicate their actions and reflections
5
•select, compare, and evaluate appropriate problem- solving strategies
•reflect on their actions and communicate their interpretations and reasoning
4
•use well-developed skills and reason flexibly, with some insight
•can construct and communicate explanations and arguments
3
•execute clearly described procedures
•apply simple problem-solving strategies
•develop short communications reporting their interpretations, results and
reasoning
2
•employ basic algorithms, formulae, procedures, or conventions
•capable of direct reasoning and literal interpretations of the results
1
•identify information and to carry out routine procedures according to direct
instructions in explicit situations.
Artifact #2 FCPS Pilot School Performance Levels
# of
Students
Tested
Mean
Score
73
539
45
489
48
503
61
522
56
553
49
464
105
443
73
567
112
680
47
558
669
540
487
Artifact #3 Falls Church HS – Climate in Mathematics Lessons
Artifact #4 FCPS Pilot Schools Compared to US PISA Schools
IN CLOSING…
• The mathematics team in ISD has
been working on performance tasks
for students at all levels.
• Summer Curriculum Projects include
task creation for grades K – Algebra 2
• Grades K – 6 already have at least
one task per quarter created.
• The mathematics team is also
continuing to focus on the 5
mathematics process goals
• Problem Solving
• Connections
• Communication
• Reasoning
• Representations
Artifact #1
What are you noticing about the
differences between the levels?
Artifact #2
What are two things that stand out?
1.
2.
Artifact #3
What comparisons can you make
about the FCHS data and other US
students? How are they different?
Artifact #4
What are you noticing about FCPS
schools and other schools in the US?