Performance Based Assessment in Mathematics

HawaiiMarch 5th, 2012

Brad OsbornBrad.osborn@pearson.com

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

What are the characteristics of students who are college and career ready?

College and Career ReadinessCollege 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 high-quality certificate program that enables students to enter a career pathway with potential future advancement.

(Educational Policy Improvement Center 2011)

Along the Way to Common Standards

College and Career Readiness

Students

(Common Core State Standards Initiative 2010c, 7)

demonstrate independence

build strong content knowledge

respond to the various demands of audience, task, purpose, and disciplinecomprehend as well as critique

value evidence

use technology and digital media strategically and capablycome to understand other perspectives and cultures

Teach Less, Learn More

Overview of the Common Core State Standards for MathematicsThe Common Core State Standards

are aligned with college and work expectations

are clear, understandable, and consistent

include rigorous content and application of knowledge through

high order skillsbuild upon strengths and lessons of current state standards

are informed by other top performing countries so that all students

are evidence-based (Common Core State Standards Initiative 2010a)

are prepared to success in our global economy and society

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 of Innovative ItemsInnovative 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

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Innovative Math Sample

Innovative Math Sample (continued)

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Sample Innovative Item

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?

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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 forMathematical 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

Common Core State Standards for Mathematics, 2010, pp.6-7

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, higher-order 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.

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, 1995

Mathematical Tasks:A Critical Starting Point for Instruction

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 Talk- Evidence of the Mathematical Practice Standards