Transcript Slide 1

Performance Based Assessment
in Mathematics
Hawaii
March 5th, 2012
Brad Osborn
[email protected]
Objectives
Participants will develop an understanding of
the Common Core State Standards
through performance tasks
Participants will identify the implications of
the CCSS assessments to instruction,
assessment, leadership and professional
development.
Along the Way to Common Standards
College and Career Readiness
College and career readiness can be defined as the
level of preparation a student needs to enroll and
succeed—without remediation—in a credit-bearing
general education course at a postsecondary
institution that offers a baccalaureate degree or
transfer to a baccalaureate program, or in a highquality certificate program that enables students to
enter a career pathway with potential future
advancement.
(Educational Policy Improvement Center
2011)
What are the characteristics of students who are
college and career ready?
Along the Way to Common Standards
College and Career Readiness
Students
demonstrate independence
build strong content knowledge
respond to the various demands of audience, task,
purpose, and discipline
comprehend as well as critique
value evidence
use technology and digital media strategically and
capably
come
to understand other perspectives and
cultures
(Common Core State Standards Initiative
2010c, 7)
Teach Less, Learn More
Overview of the Common Core
State Standards for Mathematics
The Common Core State Standards
are aligned with college and work expectations
are clear, understandable, and consistent
include rigorous content and application of knowledge thro
high order skills
build upon strengths and lessons of current state standard
are informed by other top performing countries so that all
are prepared to success in our global economy and society
are evidence-based
(Common Core State Standards Initiative
2010a)
Innovative Items
Items in which students manipulate graphic elements to
provide a response
Delivered by a computer
Scored electronically
May have multiple correct answers
Cannot be easily translated to paper
Benefits
Innovative
Itemsof Innovative Items
Assess content in different more engaging ways
Measure a broader range of skills
Allow for more authentic alignment with learning situations
Include process skills and higher-order thinking skills
Improve presentation of complex and dynamic information
Reduce reading load through visual supports
Reduce effect of successful guessing
Allow for rapid electronic scoring of open-ended items
7
Innovative Math Sample
Innovative Math Sample (continued)
Sample Innovative Item
9
Salary problem
After receiving 4.3% salary increase, a
teacher’s aide is now earning $34,000 per
year. What did she earn last year?
•
Show your strategy and make a model
•
Explain how you know your solution process is correct.
The Cube
What is the volume of a cube
whose edges each measure 3
centimeters?
What is the surface area of a
cube whose edges each
measure 3 centimeters?
A student named Eddie says,
“No matter what size the cube
is, the number you get when
you calculate its surface area is
always twice as big as the
number you get when you
calculate its volume.”
Is Eddie right? Show how you
know.
Performance Tasks
What did you notice about this task?
What are students being asked to demonstrate?
How does this align with what you are currently doing?
12
What do we want students to perform
Standards for understanding- the content standards are very
specific about what students need to understand, and even
differentiate the learning continuum between developing
understanding and understanding
Standards for performance- what students should be able to do
with their standard for understanding, how they
demonstrate their understanding
Standards for Mathematical Practice: varieties of expertise that
math educators should seek to develop in their students.
Standards for
Mathematical Practice
1.
Make sense of problems and persevere in solving
them
2.
Reason abstractly and quantitatively
3.
Construct viable arguments and critique the
reasoning of others
4.
Model with mathematics
5.
Use appropriate tools strategically
6.
Attend to precision
7.
Look for and make use of structure
8.
Look for and express regularity in repeated
reasoning
Performance tasks typically . . .
Are open-ended
Have more than one way to answer correctly
Require active performance rather than passive
reaction
Need a scoring guide or rubric
Good Performance Tasks
Are clear and unambiguous
Set parameters for what the answer should look
like
Measure something important
Are not a simple substitute for a multiple-choice
question
Require reasoning, synthesis, evaluation, higherorder thinking
Very Complex Tasks
What’s the demand on the students?
What knowledge and skills are tapped into?
What is the cognitive challenge or depth of
knowledge demand?
Is this task different from the typical tasks given to
students in your class/school/district now?
How do you think students in our schools today
would react to these kinds of tasks?
How would you approach teaching this?
Discuss at your table and report out.
Sample Performance Item- What grade level?
Sample Performance Item- What grade level?
Sample Performance Item- What grade level?
Sample Performance Item- What grade level?
Sample Performance Item- What grade level?
Sample High School Task
LUCKY DIP
25¢ a chance
3 balls the same color
Win $5
Ann is in charge of a Lucky Dip to raise money for charities. There are 3
barrels, and each contains an equal number of red, green, white, and
black balls. The balls are buried in sawdust so that you cannot see
them before you pick one out.
To play the game, you give Ann your 25¢, then you pick one ball from
each barrel.
You win $5 if all three balls are the same color.
a)
Calculate the probability that you will win the $5 if you play once.
b)
Do you think that the Lucky Dip will raise money for the local charities.
Show your calculations.
c)
Ann wants to change the game increase the amount of money it makes
for the charities.
Describe two different kinds of changes that she could make to the Lucky
Dip and find how much is likely to be raised for the charities after each
change.
Sample High School Task
PRICE REDUCTION
A.
Two for the price of one
B.
Buy one and get 25% off the second
C.
Buy two, get 50% off the second one
D.
Three for the price of two
1. Which of these four different offers gives the biggest price reduction?
_____________________________________________________________________
Explain your reasoning clearly:
_____________________________________________________________________
_____________________________________________________________________
_____________________________________________________________________
2. Which of these four different offers gives the smallest price reduction?
_____________________________________________________________________
Explain your reasoning clearly:
_____________________________________________________________________
Sample High School Task
You have the job of organizing a table tennis league.
7 players will take part.
All matches are singles.
Every player has to play each of the other players once.
There are four tables at the club.
Games will take up to half an hour.
The first match will start at 1:00 p.m.
Plan how to organize the league so that the tournament will
take the shortest possible time. Put all the information on a
poster so that the players can easily understand what to do.
Sample High School Task
The Fresha Drink Company is marketing a new soft drink.
The drink will be sold in a can that holds 200 cm3.
In order to keep costs low, the company wants to use the
smallest amount of aluminum.
Find the radius and height of a cylindrical can that holds 200
cm3 and uses the smallest amount of aluminum.
Implications
Discuss in your groups the implications for teaching and
learning?
Be prepared to share out.
Mathematical Tasks:
A Critical Starting Point for Instruction
There is no decision that teachers
make that has a greater impact on
students’ opportunities to learn and on
their perceptions about what
mathematics is than the selection or
creation of the tasks with which the
teacher engages students in studying
mathematics.
Lappan & Briars,
Going Deeper
Session A: Evidence of Mathematical Practices in Student Work
Session B: Developing an Instructional Model to Support the
Mathematical Practice Standards
Session C: Complex Math Tasks Lead to Accountable TalkEvidence of the Mathematical Practice Standards