Transcript Mathematics Assessment and Performance Tasks Jane Liang, Ed.D. Mathematics Consultant California Assessment of Student Performance and Progress (CAASPP) Office California Department of Education Pre-Good Teaching Conference Seminar California.

Mathematics Assessment and
Performance Tasks
Jane Liang, Ed.D.
Mathematics Consultant
California Assessment of Student Performance and
Progress (CAASPP) Office
California Department of Education
Pre-Good Teaching Conference Seminar
California Teachers Association
San Jose, California
January 10, 2014
CALIFORNIA DEPARTMENT OF EDUCATION
Tom Torlakson, State Superintendent of Public Instruction
Topics
TOM TORLAKSON
State Superintendent
of Public Instruction
• Overview of Smarter Balanced
mathematics assessment blueprints
• Overview of performance task
features
• Access and administration of
performance tasks
• Example of a mathematics
performance task
2
Objectives
TOM TORLAKSON
State Superintendent
of Public Instruction
• Understand Smarter Balanced
assessment in mathematics
• Understand performance tasks
• Incorporate performance tasks in
mathematics instruction
3
Smarter Balanced Mathematics Assessment Claims
4
TOM TORLAKSON
Proposed Reporting Categories
for Summative Mathematics
Assessment
State Superintendent
of Public Instruction
Total Mathematics Composite Score
Claim #1:
Concepts and
Procedures
Claim #2:
Problem
Solving Score
Claim #3:
Communicating
Reasoning
Score
Claim #4:
Modeling and
Data Score
Score 1
Score 2*
Score 3
Score 2*
Overall math score
*Claim 2 (Problem Solving) and Claim 4 (Modeling and Data Analysis) have been
combined because of content similarity and a desire to reduce test length. There are
still four claims, but only an overall math score and 3 claim scores will be reported.
5
Assessment Targets
TOM TORLAKSON
State Superintendent
of Public Instruction
• Each claim is accompanied by a set
of assessment targets that provide
more detail about the range of
content and Depth of Knowledge
(DOK) levels.
• Targets are intended to support the
development of high-quality items
and tasks that contribute evidence to
the claims.
6
Webb’s Depth of Knowledge
The levels of complexity of the cognitive demand:
‒ Level 1: Recall and Reproduction
• Requires eliciting information such as a fact, definition, term,
or a simple procedure, as well as performing a simple algorithm
or applying a formula.
– Level 2: Basic Skills and Concepts
• Requires the engagement of some mental processing beyond
a recall of information.
– Level 3: Strategic Thinking and Reasoning
• Requires reasoning, planning, using evidence, and explanations
of thinking.
– Level 4: Extended Thinking
• Requires complex reasoning, planning, developing, and
thinking most likely over an extended period of time.
Targets for Claim #1,
Concepts and Procedures
TOM TORLAKSON
State Superintendent
of Public Instruction
• Assessment targets for claim #1 are
grade/subject level dependent.
• Targets are the cluster-level headings
of the content standards in the
Common Core State Standards for
Mathematics (CCSS-M).
• Smarter Balanced designations
– Major [m] clusters
– Additional/supporting [a/s] clusters
8
TOM TORLAKSON
State Superintendent
of Public Instruction
Targets for Claim #1,
Concepts and Procedures
(cont.)
Example of targets for grade 3:
• Target A [m]: Use the four operations with
whole numbers to solve problems. (DOK 1, 2)
• Target B [a/s]: Gain familiarity with factors and
multiples. (DOK 1)
• Target C [a/s]: Generate and analyze patterns.
(DOK 2, 3)
• Target D [m]: Generalize place value
understanding for multi-digit whole numbers.
(DOK 1, 2)
9
Targets for Claims #2, #3,
and #4
TOM TORLAKSON
State Superintendent
of Public Instruction
• Claims #2, #3, and #4 are aligned
to the Mathematics Practice
Standards (MPS) from the CCSSM.
• Assessment targets for claims #2,
#3, and #4 are consistent across
grade/subject levels.
10
Targets for Claim #2
Problem Solving
TOM TORLAKSON
State Superintendent
of Public Instruction
• Target A: Apply mathematics to solve wellposed problems arising in everyday life,
society, and the workplace. (DOK 2, 3)
• Target B: Select and use appropriate tools
strategically. (DOK 1, 2)
• Target C: Interpret results in the context of a
situation. (DOK 2)
• Target D: Identify important quantities in a
practical situation and map their relationships
(e.g., using diagrams, two-way tables, graphs,
flowcharts, or formulas). (DOK 1, 2, 3)
11
Targets for Claim #3
Communicating and Reasoning
TOM TORLAKSON
State Superintendent
of Public Instruction
• Target A: Test propositions or conjectures with
specific examples. (DOK 2)
• Target B:Construct, autonomously, chains of
reasoning that will justify or refute propositions
or conjectures. (DOK 3, 4)
• Target C: State logical assumptions being used.
(DOK 3)
• Target D: Use the technique of breaking an
argument into cases. (DOK 2, 3)
12
TOM TORLAKSON
State Superintendent
of Public Instruction
Targets for Claim #3
Communicating and Reasoning
(cont.)
• Target E: Distinguish correct logic or reasoning
from that which is flawed, and–if there is a flaw
in the argument–explain what it is. (DOK 2, 3, 4)
• Target F: Base arguments on concrete referents
such as objects, drawings, diagrams, and
actions. (DOK 2, 3)
• Target G: At later grades, determine conditions
under which an argument does and does not
apply. (For example, area increases with
perimeter for squares, but not for all plane
figures.) (DOK 3, 4)
13
Targets for Claim #4
Modeling and Data Analysis
TOM TORLAKSON
State Superintendent
of Public Instruction
• Target A: Apply mathematics to solve
problems arising in everyday life, society, and
the workplace. (DOK 2, 3)
• Target B:Construct, autonomously, chains of
reasoning justify mathematical models used,
interpretations made, and solutions proposed
for a complex problem. (DOK 2, 3, 4)
• Target C: State logical assumptions being
used. (DOK 1, 2)
• Target D: Interpret results in the context of a
situation. (DOK 2, 3)
14
TOM TORLAKSON
State Superintendent
of Public Instruction
Targets for Claim #4
Modeling and Data Analysis
(cont.)
• Target E: Analyze the adequacy of and make
improvements to an existing model or develop
a mathematical model of a real phenomenon.
(DOK 3, 4)
• Target F: Identify important quantities in a
practical situation and map their relationships
(e.g., using diagrams, two-way tables, graphs,
flowcharts, or formulas). (DOK 1, 2, 3)
• Target G: Identify, analyze, and synthesize
relevant external resources to pose or solve
problems. (DOK 3, 4)
15
Smarter Balanced Assessment:
Technology
TOM TORLAKSON
State Superintendent
of Public Instruction
• Computer-based testing
– Tests are administered
electronically.
• Computer adaptive testing
(CAT)
– Item difficulties are adjusted to
each student’s performance.
16
Smarter Balanced
Assessment: Item Types
TOM TORLAKSON
State Superintendent
of Public Instruction
Using various types of items and
tasks to connect mathematics
content and practice standards:
•
•
•
•
•
Selected response (SR)
Short constructed response (CR)
Extended constructed response (ECR)
Technology enhanced (TE)
Performance tasks (PT)
17
Smarter Balanced Preliminary Mathematics Assessment Blueprint
18
Smarter Balanced Preliminary Mathematics Assessment Blueprint (cont.)
P(6)=1.0 indicates that each student will have a 100% probability of receiving at least 6 CAT items.
19
Smarter Balanced Preliminary Mathematics Assessment Blueprint (cont.)
20
Smarter Balanced Preliminary Mathematics Assessment Blueprint (cont.)
21
TOM TORLAKSON
State Superintendent
of Public Instruction
Source:
http://sbac.portal.airast.org/Pilot_Test/reources/Training_Modules/Flash/SBAC_Training_Module_5/SBAC_Training_Module_5.ht
m
22
Components of Mathematics
Performance Tasks
TOM TORLAKSON
State Superintendent
of Public Instruction
• Stimulus presentation
• Information process
23
Types of Smarter Balanced
Performance Tasks
TOM TORLAKSON
State Superintendent
of Public Instruction
1. Performance task only
• Task overview
• Student task
2. Classroom activity plus performance
task
• Task overview
• Classroom activity
• Student task
24
Classroom Activity
TOM TORLAKSON
State Superintendent
of Public Instruction
• As part of its research agenda during the pilot test,
Smarter Balanced is exploring the implementation of a
classroom-based activity prior to the individually
administered and scored portion of the performance task.
• The purpose of the classroom activity is to reduce the
experiential bias of the task context across test takers
and level the playing field for students.
– For example, in a task about horseback riding, we
would want to introduce any potentially unfamiliar
terms about horseback riding unrelated to the
construct (e.g., mathematics).
• Existing and ongoing research will inform the
consortium’s decision about whether to include the
classroom-based activities during the live summative
assessment in 2015.
25
TOM TORLAKSON
State Superintendent
of Public Instruction
TA: task administrator
26
TOM TORLAKSON
State Superintendent
of Public Instruction
27
Example of a Performance Task
TOM TORLAKSON
State Superintendent
of Public Instruction
28
TOM TORLAKSON
State Superintendent
of Public Instruction
29
TOM TORLAKSON
State Superintendent
of Public Instruction
30
Sample Performance
Task: Taking a Field Trip
TOM TORLAKSON
State Superintendent
of Public Instruction
1.
2.
3.
4.
5.
Classroom activity
Setting the context
Student task
Task specifications
Scoring rubric
31
Classroom Activity
TOM TORLAKSON
State Superintendent
of Public Instruction
Some suggestions for turning “Taking a Field
Trip” into a rich, classroom-based learning task:
• Change the information to reflect locations that are
within driving distance of your school.
• Ask students to collect the necessary information to
inform the important variables.
– How far is each location?
– How many does a bus hold? What is the cost?
– How much will we have to pay to enter? Are
teachers and other adults free?
• Collect student data on preferences for these locations
similar to the provided data in the task.
32
Setting the Context
TOM TORLAKSON
State Superintendent
of Public Instruction
• Engage students
– Ask things students like about field
trips: volunteering responses, 2minute pair share, summary on board
• Select a place
– Ask students to nominate places for
polling list: 2 rounds of vote
• Consider other issues
– Proximity, safety, etc.
• Calculate costs
33
Student Task
TOM TORLAKSON
State Superintendent
of Public Instruction
Determine where the class should
go on the field trip based on
• The survey results
• The cost per student
34
Survey Results
TOM TORLAKSON
State Superintendent
of Public Instruction
35
Question 1
TOM TORLAKSON
State Superintendent
of Public Instruction
Based only on the results of the
class votes, where would you
recommend the class go on the field
trip? Show your work or explain how
you found your answer.
36
Distance Map
TOM TORLAKSON
State Superintendent
of Public Instruction
37
Cost Chart
TOM TORLAKSON
State Superintendent
of Public Instruction
38
Cost Considerations
TOM TORLAKSON
State Superintendent
of Public Instruction
• The teacher and parent helpers do not
pay an entrance fee.
• There are 30 students in the class.
• Only 1 bus is needed.
• The bus charge is for the entire busload
of students (not for each student).
• Each student will pay the same amount.
• The school will pay the first $200 of the
trip.
39
Question 2
TOM TORLAKSON
State Superintendent
of Public Instruction
How much will each student pay to
go on each trip? Show your work or
explain how you found your answer.
40
Question 3
TOM TORLAKSON
State Superintendent
of Public Instruction
Daniel thinks that it will cost less to
go to the zoo because the entrance
fee is only $2.50 per person. Explain
why you agree or disagree with
Daniel’s thinking.
41
Final Task
TOM TORLAKSON
State Superintendent
of Public Instruction
Write a short note to your teacher
stating where you think the class
should go on its field trip, based on
how you would evaluate all the
different factors, including student
votes, costs, distance, and what you
think would be fun.
42
TOM TORLAKSON
State Superintendent
of Public Instruction
43
Sample Performance Task
Scoring Criteria
TOM TORLAKSON
State Superintendent
of Public Instruction
44
Sample Performance Task
Scoring Criteria (cont.)
TOM TORLAKSON
State Superintendent
of Public Instruction
45
Resources
TOM TORLAKSON
State Superintendent
of Public Instruction
• Smarter Balanced Web Site:
http://www.smarterbalanced.org/
• California Department of Education Smarter
Balanced Web Page:
http://www.cde.ca.gov/ta/tg/sa/smarterbalance
d.asp
• Subscribe to CDE Smarter Balanced listserv
by sending a blank e-mail to:
[email protected]
46
Questions and Answers
TOM TORLAKSON
State Superintendent
of Public Instruction
Jane Liang, Ed.D.
Mathematics Consultant
California Assessment of Student Performance and Progress
(CAASPP) Office
California Department of Education
[email protected]
916-322-1854
47