RUBRICS

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· Using Scoring Rubrics (Mary Allen). Below is a discussion about rubrics in general.

Rubrics are explicit schemes for classifying products or behaviors into categories that vary along a continuum. They can be used to classify virtually any product or behavior, such as essays, research reports, portfolios, works of art, recitals, oral presentations, performances, and group activities. Judgments can be self-assessments by students; or judgments can be made by others, such as faculty, other students, or field-work supervisors. Rubrics can be used to provide formative feedback to students, to grade students, and/or to assess programs.

There are two major types of rubrics:
- Holistic rubric (one global, holistic rating for a product or behavior)
- Analytic rubric (separate, holistic ratings of specified characteristics of a product or behavior)

Rubrics have many strengths:
- Complex products or behaviors can be examined efficiently.
- Developing a rubric helps to precisely define faculty expectations.
- Well-trained reviewers apply the same criteria and standards, so rubrics are useful for assessments involving multiple reviewers.
- Summaries of results can reveal patterns of student strengths and areas of concern.
- Helps students understand the meaning behind their grades.
- Improves student performance.
- Rubrics are criterion-referenced, rather than norm-referenced. Raters ask, "Did the student meet the criteria for level 5 of the rubric?" rather than "How well did this student do compared to other students?" This is more compatible with cooperative and collaborative learning environments than competitive grading schemes and is essential when using rubrics for program assessment because you want to learn how well students have met your standards.
- Ratings can be done by students to assess their own work, or they can be done by others, such as peers, fieldwork supervisions, or faculty.

Developing a Rubric
- Identify what you are assessing (e.g., critical thinking).
- Identify the characteristics of what you are assessing (e.g., appropriate use of evidence, recognition of logical fallacies).
- Describe the best work you could expect using these characteristics. This describes the top category.
- Describe the worst acceptable product using these characteristics. This describes the lowest acceptable category.
- Describe an unacceptable product. This describes the lowest category.
- Develop descriptions of intermediate-level products and assign them to intermediate categories. You might develop a scale that runs from 1 to 5 (unacceptable, marginal, acceptable, good, outstanding), 1 to 3 (novice, competent, exemplary), or any other set that is meaningful.
- Ask colleagues who were not involved in the rubric's development to apply it to some products or behaviors and revise as needed to eliminate ambiguities.

Suggestions for Using Scoring Rubrics for Grading and Program Assessment
- Hand out the grading rubric with an assignment so students will know your expectations and how they'll be graded. This should help students master your learning objectives by guiding their work in appropriate directions.
- Use a rubric for grading student work, including essay questions on exams, and return the rubric with the grading on it. Faculty save time writing extensive comments; they just circle or highlight relevant segments of the rubric. Each row in the rubric could have a different array of possible points, reflecting its relative importance for determining the overall grade. Points (or point ranges) possible for each cell in the rubric could be printed on the rubric, and a column for points for each row and comments section(s) could be added.
- Develop a rubric with your students for an assignment or group project. Students can then monitor themselves and their peers using agreed-upon criteria that they helped develop. (Many faculty find that students will create higher standards for themselves than faculty would impose on them.)
- Have students apply your rubric to some sample products (e.g., lab reports) before they create their own. Faculty report that students are quite accurate when doing this, and this process should help them evaluate their own products as they develop them.
- Have students exchange paper drafts and give peer feedback using the rubric, then give students a few days before the final drafts are turned in to you. (You might also require that they turn in the draft and scored rubric with their final paper.)
- Have students self-assess their products using the grading rubric and hand in the self-assessment with the product; then faculty and students can compare self- and faculty-generated evaluations.
- Use the rubric for program assessment. Faculty can use it in classes and aggregate the data across sections, faculty can independently assess student products (e.g., portfolios) and then aggregate the data, or faculty can participate in group readings in which they review student products together and discuss what they found. Field-work supervisors or community professionals also may be invited to assess student work using rubrics. A well-designed rubric should allow evaluators to efficiently focus on specific learning objectives while reviewing complex student products, such as theses, without getting bogged down in the details. Rubrics should be pilot tested, and evaluators should be "normed" or "calibrated" before they apply the rubrics (i.e., they should agree on appropriate classifications for a set of student products that vary in quality). If two evaluators apply the rubric to each product, inter-rater reliability can be examined. Once the data are collected, faculty discuss results to identify program strengths and areas of concern, "closing the loop" by using the assessment data to make changes to improve student learning.
- Faculty can get "double duty" out of their grading by using a common rubric that is used for grading and program assessment. Individual faculty may elect to use the common rubric in different ways, combining it with other grading components as they see fit.

· How to create rubrics.

Here are examples and strategies for developing rubrics in general.

Here

· Here is a simple rubric for use in mathematics. You can get more related details here . Materials on CD-ROM can be purchased here.

Level	Understanding	Strategies, Reasoning, Procedures	Communication
Novice	There is no solution, or the solution has no relationship to the task. Inappropriate concepts are applied and/or procedures are used. The solution addresses none of the mathematical components presented in the task.	No evidence of a strategy or procedure, or uses a strategy that does not help solve the problem. No evidence of mathematical reasoning. There were so many errors in mathematical procedures that the problem could not be resolved.	There is no explanation of the solution, the explanation cannot be understood or it is unrelated to the problem. There is no use or inappropriate use of mathematical representations (e.g. figures, diagrams, graphs, tables, etc.). There is no use, or mostly inappropriate use, of mathematical terminology and notation.
Apprentice	The solution is not complete indicating that parts of the problem are not understood. The solution addresses some, but not all of the mathematical components presented in the task.	Uses a strategy that is partially useful, leading some way toward a solution, but not to a full solution of the problem. Some evidence of mathematical reasoning. Could not completely carry out mathematical procedures. Some parts may be correct, but a correct answer is not achieved.	There is an incomplete explanation, it may not be clearly presented. There is some use of appropriate mathematical representation. There is some use of mathematical terminology and notation appropriate of the problem.
Practitioner	The solution shows that the student has a broad understanding of the problem and the major concepts necessary for its solution. The solution addresses all of the components presented in the task.	Uses a strategy that leads to a solution of the problem. Uses effective mathematical reasoning. Mathematical procedures used. All parts are correct and a correct answer is achieved.	There is a clear explanation. There is appropriate use of accurate mathematical representation. There is effective use of mathematical terminology and notation.
Expert	The solution shows a deep understanding of the problem including the ability to identify the appropriate mathematical concepts and the information necessary for its solution. The solution completely addresses all mathematical components presented int he task. The solution puts to use the underlying mathematical concepts upon which the task is designed.	Uses a very efficient and sophisticated strategy leading directly to a solution. Employs refined and complex reasoning Applies procedures accurately to correctly solve the problem and verify the results. Verifies solution and/or evaluates the reasonableness of the solution. Makes mathematically relevant observations and/or connections.	There is a clear, effective explanation de- tailing how the problem is solved. All of the steps are included so that the reader does not need to infer how and why decisions were made. Mathematical representation is actively used as a means of communicating ideas related to the solution of the problem. There is precise and appropriate use of mathematical terminology and notation.

· More sample rubrics for use in mathematics.

HOLISTIC SCALES

California Generalized Rubric for Math (Source: California State Department of Education, A Question of Thinking. Sacramento, CA: California State Department of Education, 1989)

Score	Label	Description
6	Exemplary response	Gives a complete response with a clear, coherent, unambiguous and elegant explanation; includes a clear and simplified diagram; communicates effectively to the identified audience; shows understanding of the open-ended problem's mathematical ideas and processes; identifies all the important elements of the problem; may include examples and counterexamples; presents strong supporting arguments.
5	Competent response	Gives a fairly complete response with reasonably clear explanations; may include an appropriate diagram; communicates effectively to the identified audience; shows understanding of the problem's mathematical ideas and processes; identifies the most important elements of the problem; presents solid supporting arguments.
4	Minor Flaws But Satisfactory	Completes the problem satisfactorily, but the explanation may be muddled; argumentation may be incomplete; diagram may be inappropriate or unclear; understands the underlying mathematical ideas; uses mathematical ideas effectively.
3	Serious Flaws But Nearly Satisfactory	Begins the problem appropriately but may fail to complete or may omit significant parts of the problem; may fail to show full understanding of mathematical ideas and processes; may make major computational errors; may misuse or fail to use mathematical terms; response may reflect an inappropriate strategy for solving the problem.
2	Begins, But Fails to Complete Problem.	Explanation is not understandable; diagram may be unclear; shows no understanding of the problem situation; may make major computational errors.
1	Unable to Begin Effectively	Words do not reflect the problem; drawings misrepresent the problem situation; copies parts of the problem but without attempting a solution; fails to indicate which information is appropriate to the problem.

Maine Holistic Rubric for Mathematics Open-Ended Items

Score	Description
4	A correct solution and an appropriate strategy are shown or explained and the solution is shown with correct label or description if necessary.
3	A complete, appropriate strategy is show or explained but: nan incorrect solution is given due to a simple computational or other error or nno solution is given. (b) A correct solution is given with no solution strategy or explanation shown. (c)A correct solution and appropriate strategy is shown or explained, but not labeled correctly when necessary.
2	(a) Some parts of an appropriate strategy are shown or explained, but some key elements are missing. (b) Some parts of an appropriate strategy are shown or explained, along with some inappropriate parts. (c) Appropriate strategy shown or explained, but implemented incorrectly.
1	Some work or explanation beyond re-copying data, but work would not lead to a correct solution. One or more incorrect approaches attempted or explained.
0	No work or solution shown or explained. Incorrect solution and no work shown or explained. Some data from the problem copied over, but no evidence of any strategy is shown or explained.

ANALYTIC SCALES

Chicago Public Schools Bureau of Student Assessment (Source: Szetela, Walter and Nicol, Cynthia. Evaluating Problem Solving in Mathematics. Educational Leadership, May 1992, pp. 42-45.)

Score	Scale 1: Undertanding the Problem	Scale 2: Solving the Problem	Scale 3: Answering the Problem
4	Complete understanding of the problem	A plan that could lead to a correct solution with no arithmetic errors
3	Misinterprets minor part of the problem	Substantially correct procedure with minor omission or procedural error
2	Misinterprets major part of the problem	Partially correct procedure but with major fault	Correct solution
1	Completely misinterprets the problem	Totally inappropriate plan	Copying error; computational error, partial answer for problem with multiple answers; no answer statement; answer labeled incorrectly
0	No attempt	No attempt	No answer or wrong answer based upon an inappropriate plan

Chicago Public Schools Bureau of Student Assessment (Source: Charles, Randall, Lester, Frank and O'Daffer, Phares. How to Evaluate Progress in Problem Solving. Reston, VA: National Council of Teachers of Mathematics, 1987. In Stenmark, Jean, Mathematics Assessment: Myths, Models, Good Questions and Practical Suggestions. Reston, VA: National Council of Teachers of Mathematics, 1991.)

Score	Scale 1: Undertanding the Problem	Scale 2: Planning a Solution	Scale 3: Answering the Problem
2	Complete understanding of the problem	Plan could have led to a correct solution if implemented properly<	Correct answer and correct label for the answer
1	Part of the problem misunderstood or misinterpreted	Partially correct plan based on part of the problem being interpreted correctly	Copying error; computational error, partial answer for problem with multiple answers
0	Complete misunderstanding of the problem	No attempt, or totally inappropriate plan	No answer or wrong answer based upon an inappropriate plan

Another sample:

Criteria

Points

	4	3	2	1
Explanation	A complete response with a detailed explanation.	Good solid response with clear explanation.	Explanation is unclear.	Misses key points.	____
Use Of Visuals	Clear diagram or sketch with some detail.	Clear diagram or sketch.	Inappropriate or unclear diagram.	No diagram or sketch.	____
Mechanics	No math errors.	No major math errors or serious flaws in reasoning.	May be some serious math errors or flaws in reasoning.	Major math errors or serious flaws in reasoning.	____
Demonstrated Knowledge	Shows complete understanding of the questions, mathematical ideas, and processes.	Shows substantial understanding of the problem, ideas, and processes.	Response shows some understanding of the problem.	Response shows a complete lack of understanding for the problem.	____
Requirements	Goes beyond the requirements of the problem.	Meets the requirements of the problem.	Hardly meets the requirements of the problem.	Does not meet the requirements of the problem.	____
Counter Examples	Includes counter examples.	a	Does not include counter examples.	yy	____
				Total---->	____

Teacher Comments:

For more sample math rubrics like these, check out this website.

· Example of alternative assignment in Calculus with scoring rubric.

Math SLO Home · General SLO Resources · Examples of Math SLOs · Math Standards · Culturally Responsive Resources

last update: 6/28/05