Using Rubrics

to Assess

Performance Tasks

in Algebra

Theresa Davis

Michiko McClaryClaflin University

Bridget ColemanUSC Aiken

SCCTM 2015 Greenville

10:30 – 11:30

November 12, 2015

Claflin UniversitySchool of Natural Sciences and Mathematics

Department of Mathematics and Computer

Science

“Assessing Student Success in College

Algebra with the Implementation of

Performance Based (STEM) Tasks”

Funding Agency:

Southern Education Foundation

Performance Tasks

Enable students to demonstrate their

ability to integrate and use knowledge,

skills, and work habits in a meaningful

activity.

Real-life applications / relevancy

Algebra Performance Tasks

(Science Integration)

Packaging Cups (Linear Relationships, Graphing)

Making the Most of Your Space (Quadratic

Functions)

Disappearing Discs (Exponential & Log Functions)

Body Mass Index (Linear Relationships, Graphing)

Hand Shake (Linear & Quadratic Equations)

Packaging Cups

Performance Task

After applying for several summer jobs to earn

money to pay for textbooks and a laptop computer, you

have been hired by Tigrex. Tigrex is a multimillion dollar

company that makes disposable drinking cups for a

popular coffee retailer. The company currently ships cups

in boxes of 100. Tigrex’s management is interested in

developing innovative packaging designs which would

save the company money.

Your team’s task is to determine the most inexpensive

method of packaging cups while using resources as

efficiently as possible.

Packaging Cups Procedure

Performance Task

1) Measure the diameter (in centimeters) of a cup at its open end. Record

the diameter.

2) Stack two cups. Measure and record the height of the two cups in the

table below.

3) Add two cups to the stack. Measure and record the height of the four

cups.

4) Add two more cups to the stack. Measure and record the height of the

six cups.

5) Add two more cups to the stack. Measure and record the height of the

eight cups.

6) Add two more cups to the stack. Measure and record the height of the

ten cups.

Number of Cups Height (cm)

2

4

6

8

10

Questions

1. What is the independent variable in this

situation? Explain how you identified the

independent variable.

2. What is the dependent variable in this

situation? Explain how you identified the

dependent variable.

Questions3. When you graph the data, do you expect a

positive correlation, negative correlation, or

neither?

4. Using your five data points, create a scatter

plot and describe the shape of your graph.

5. Pick two points and find the slope of a “best

fit” line for these data points.

6. What is the unit for the slope?

7. What does the slope represent in this

problem?

Math

Science

SCCR Standards

Student Comments

“There was an incorporation of science. This can

relate to daily life, because it could go with

problem solution.”

“Other than math we used English and reading to

solve the problem.”

“A construction worker could use

Probability/Statistics to measure materials and use

a system where you have to graph your

information.”

“You could compare this to everyday life by

determining how to place a certain amount of

dishes on a shelf.”

Student Comments

“In life you have to look at situations differently. We

cannot control the height of cups but we can

control the number of cups”

“We could use this for an inventory job to help

when we have to stock the merchandise and

count for each material on the shelves.”

“We did not use any other strategy.”

“I honestly feel like we didn't use any other subject.

However, I can relate this to my daily life because

we used teamwork and had to analyze the

problem.”

How do you assess your

students’ performance?

How would you assess this?

How would you assess this?

Rubrics are rating scales-as opposed to checklists-that

are used with performance assessments.

They are formally defined as scoring guides, consisting of

specific pre-established performance criteria, used in

evaluating student work on performance assessments.

Rubrics are typically the specific form of scoring

instrument used when evaluating student performances

or products resulting from a performance task.

Restaurant Quality

Make a list of qualities you require of a

restaurant for you to eat there?

What makes one restaurant your favorite

and another your least favorite?

Assess these restaurants:

Popeye's, Red Lobster, Outback, Subway

Think-Pair-Share

Developing a Rubric

A constructed list of characteristics used as criteria

for ranking the quality of students’ work along with

a guide for scoring or grading.

A combination of performance criteria and a

holistic evaluation of students’ performance on the

criteria.

Rubrics

Rubrics

Rubrics

focus on measuring a stated objective

(performance, behavior, or quality)

use a range to rate performance

contain specific performance characteristics

arranged in levels indicating either the

developmental complexity of the strategy used or

the degree to which a standard has been met

Criteria

Exemplary

Target

Expert

Meets

Expectations,

Proficient

Acceptable

Practitioner

Below

Expectations,

Apprentice

Unacceptable,

Novice

Quality of Work

Ele

me

nts

to

Sc

ore

Rubric Template

Got it! Not there yet!

Generic Math

Problem-Solving Rubric

Descriptors and Performance Levels Use measurable criteria.

Specify the quality (or absence) vs. comparatives (“not as thorough

as”) or value language (“excellent content”)

Use key, teachable “criteria” (Emphasize what counts)

Specifically define levels of quality. (Avoid vague descriptors.)

Concrete versus abstractEx. Organization: sharply focused thesis, topic sentences clearly

connected to thesis, logical ordering of paragraphs, conclusion

ends with clincher

“poorly organized”

Key Question to ask yourself: What does it look like?

Tips For Effective Rubric Design

design a rubric that does its job

write precise criteria and descriptors

make your rubric student-friendly

Tips

Limit the number of criteria

List independent criteria separately

Avoid combing independent criteria

“very clear” and “very organized” (may be

clear but not organized or vice versa).

Aim for an even number of levels

Create continuum between least and most

Define poles and work inward

List skills and traits consistently across levels

Caution:

Don’t let the rubric stand alone.

Provide specific “Comments” on your rubric

and/or on the student product itself.

Claflin Rubric Template

The Performance Task

Assignment Sheet

The instructions on the assignment sheet are important.

Connect to the rubric (Use same language!)

The lawyers in your class

“But the rubric doesn’t say that…”

It’s hard work…

Expect to revise…and revise…

“There are no final versions, only drafts

and deadlines.”

When you’ve got a good one, SHARE IT!

Performance Task

Benefits & Impact

Improved learning in Algebra (Cognitive)

Improved attitudes toward math (Affective)

Independent thinkers

Meaningful/relevant contexts

Interdisciplinary Connections

Consistent across class sections

Increased student attendance

Resources for Math

Performance Tasks Navigations Series by NCTM (nctm.org)

Mathematics Teacher(nctm.org)

Mathematics Teaching in the Middle

School (nctm.org)

Determining Functions Using Regression:

What's the Function?

http://Illuminations.nctm.org/Lesson.aspx?id

=4144

Resources for Rubrics

On-line Rubric Generators

Rubistar

rubistar.4teachers.org

Teach-nology

www.teach-nology.com

iRubric

http://www.rcampus.com/indexrubric.cfm

Recipes4Success

Resources

For more information:

Claflin University

Theresa Davis, tdavis@claflin.edu

Michiko McClary, mmcclary@claflin.edu

USC Aiken

Bridget Coleman, BridgetC@usca.edu