ksc mathematics creating rubrics for assessment of general education mathematics dick jardine suny...
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KSC Mathematics
Creating Rubrics for Assessment of General Education Mathematics
Dick Jardine
SUNY General Education Assessment Conference
Syracuse, NY
April 27, 2005
KSC Mathematics
Overview
• The language of rubrics• Some examples• Make your own rubric!• What to do with the results
KSC Mathematics
What is a rubric?
•A rubric is a scoring device designed to assist in the process of communicating expectations and assessing performance
•Based on a range of criteria rather than a single numerical score
•A working guide for both students and faculty
•Non-traditional, “authentic” assessment instrument
KSC Mathematics
Analytic and Holistic Rubrics
Analytic:• Identify and assess
components of the task
• A score for each component
• Provide more detail about standards
Holistic:• Assesses the
whole work• One score for the
entire product
KSC Mathematics
Holistic Rubric Template
Criterion Score
KSC MathematicsExample holistic rubricStudent will conduct a hypothesis test4 Uses appropriate test with correct with correct
interpretation. Identifies correct null and alternative hypothesis. Uses correct test statistic. Obtains correct p-value and correctly interprets that result in terms of the null hypothesis and the context with clear exposition.
3 Provides most of level 4 but with unclear/incorrect interpretation
2 Uses incorrect test but remaining work follows from error1 Uses incorrect test and remaining work does not follow
0 Little or no work of value
KSC Mathematics
Holistic rubric for hypothesis test
Criterion Score
Uses appropriate test with correct interpretation. Identifies correct null and alternative hypothesis…
4
Provides most of level 4 but with unclear/incorrect interpretation
3
Uses incorrect test but remaining work follows from error
2
Uses incorrect test and remaining work does not follow
1
Little or no work of value 0
KSC Mathematics
Analytic and Holistic Rubrics
Analytic:• Identify and
assess components
• A score for each component
• Provide more detail about standards
Holistic:• Assesses the
whole work• One score for the
entire product
KSC Mathematics
Analytic Rubric Template
Score
Criterion
0 1 2
KSC Mathematics
Problem solving evaluation matrix
0 1 2 3
Identify appropriate variables
No attempt Inappropriate variable definition
Appropriate variables defined imprecisely
Appropriate variables defined precisely w/units
Organize available information
No attempt Inappropriate attempt
Incomplete attempt Appropriate attempt with clear explanation
Model the problem mathematically
No attempt Inappropriate attempt
Appropriate attempt with minor errors
Appropriate attempt with no errors
Execute the model No attempt Inappropriate attempt
Appropriate attempt with arithmetic errors
Appropriate method with no errors
Evaluatethe results No attempt An attempt but fails to explain solution, provide units
Incomplete explanation Complete explanation with correct labeling
Problem solving matrix (Rhodes State College)
KSC MathematicsProblem solving evaluation scoresheet
Score Comments
Identify appropriate variables
Organize available information
Model the problem mathematically
Execute the model
Evaluate the results
Total
KSC Mathematics
Possible terms for scoring levels• Needs Improvement...Satisfactory...Good…
Exemplary
• Beginning...Developing...Accomplished…Exemplary
• Needs work...Good…Excellent
• Novice...Apprentice...Proficient…Distinguished
• Numeric scale ranging from 0 to n
KSC Mathematics
Course-embedded assessment(University of Northern Colorado)
•Align course objectives with Gen Ed
outcomes
•Identify course objectives and student
outcomes
•Explain tasks to measure each
objective/outcome
•Explain performance criteria to evaluate each
objective (what constitutes meeting
expectations)
KSC Mathematics
Course objective Advanced Proficient In Progress Not Assessable
1. Student will demonstrate proficiency in the use of math/stats to structure their understanding of and investigate questions in the world around them
2. The student will demonstrate proficiency in treating math/stats content at an appropriate level
3. The student will demonstrate competence in the use of numerical, graphical, and algebraic representations
4. The student will demonstrate proficiency in the use of math/stats in written and oral from.
5. The student will demonstrate proficiency in the use of math/stats to formulate and solve problems
6. The student will demonstrate proficiency in the use of technology to support their use of math/stats
KSC Mathematics
Area 1 : The student will demonstrate proficiency in the use of mathematics and/or statistics to structure their understanding of and investigate questions in the world around them
Task: (Test question) How long will it take for $8600 to grow to $31,300 at an interest rate of 5.5% if the interest is compounded continuously?
Student uses logarithms and rounds for a reasonable answer
4
Student uses logarithms and gives answer copied from calculator
3
Student uses logarithms but incorrectly
2
Student uses guess and check 1
No effort 0
Exceedsexpectations
Meetsexpectations
Does not meetexpectations
KSC Mathematics
Performance Assessment Scoring Rubric
4 – Thorough Understanding•Demonstrates a thorough understanding of the concepts/content •Demonstrates mastery of the strategies and skills•Solves new problems by creative and appropriate use of knowledge/skills
3 – Good understanding•Demonstrates a satisfactory understanding•Carries out skills and strategies with few minor errors •Applies prior knowledge when prompted
2 – Satisfactory understanding•Demonstrates partial understanding of most important concepts•Carries out skills and strategies with minor errors•Makes progress toward the solving of new problems
1 – Needs improvement•Demonstrates weak understanding of concepts/content•Carries out skills and strategies with significant critical errors
KSC Mathematics
Developing your own rubrics
• With a colleague:o Determine the learning objective to be assessed.o List the criteria to be evaluated. o Describe degrees of quality (in a matrix),
starting with the best and worst quality and then filling in the middle.
• Share the rubric with students before they complete the assignment so students understand the criteria for evaluation.
• With a colleague:o Use the rubric to evaluate the students’ work to
determine if they have met the learning objective.
o Adjust rubric as needed for next assessment
KSC Mathematics
Some limitations of rubrics
• Time it takes to develop quality rubrics
• Reduction of “knowledge rich” activities to selected easily observable behaviors
• Achieving consensus to “norm” the rubric standards
KSC Mathematics
Some advantages of rubrics
• Faculty provide focus, emphasis, and attention to details for students
• Students have explicit details regarding teacher expectations
• Tool for student development• Grading more efficient and effective
KSC Mathematics
What to do with the results?
• Improve student learning
• Improve curriculum and instruction
• Improve assessment process
• How to use the numbers?
KSC Mathematics
Summary and conclusion
• Creating rubrics should be a collaborative process
• Communicate the standards to students • Calibrating the scoring requires significant
discussion• Improve learning with the results• http://www.maa.org/saum
email: [email protected]