Standards and Rubrics for Assessing Learning Outcomes in Mathematics

1. Standards and Rubrics for Assessing Learning Outcomes in Mathematics GEAR Conference April 27th – 28th

2. Presenters:Maryann Faller – Adirondack CCRalph Bertelle – Columbia-Greene CCJack Narayan – SUNY Oswego

3. History • The SUNY Board of Trustees passed a resolution creating three levels of assessment: general education, assessment of the major and system-wide assessment. • PACGE (Provost’s Advisory Council on General Education) was formed to provide some guidance to the campuses as they submitted the courses they wanted to use for general education in mathematics.

4. PACGE developed the Guidelines for the Approval of State University General Education Requirement Courses which listed the following learning outcomes for mathematics. Students will show competence in the following quantitative reasoning skills: • Arithmetic; • Algebra; • Geometry; • Data analysis; and • Quantitative reasoning

5. GEAR (General Education Assessment Review) was formed to assist campuses in assessing the learning outcomes in general education. • ACGE (Advisory Council on General Education) was formed to serve as the judicator for general education courses and to review/revise the learning outcomes. • SUNY BoT passes a resolution requiring strengthened campus-based assessment in mathematics, basic communication and critical thinking.

6. At the request of the mathematics faculty from our campuses and the Provost, ACGE revises the learning outcomes in mathematics. New Learning Outcomes in Mathematics Students will demonstrate the ability to: • interpret and draw inferences from mathematical models such as formulas, graphs, tables and schematics; • represent mathematical information symbolically, visually, numerically and verbally; • employ quantitative methods such as, arithmetic, algebra, geometry, or statistics to solve problems;   • estimate and check mathematical results for reasonableness; and   • recognize the limits of mathematical and statistical methods.

7. There are three options for assessing the learning outcomes in mathematics. • Nationally-normed standardized tests • SUNY-normed standardized tests • Using rubrics developed by discipline specific panels. The discipline panels first met at System Administration on February, 2005 to discuss the charge and other aspects of writing those rubrics.

8. Members of the Mathematics Discipline Panel • Maryann Faller – Chair, Adirondack CC • Mel Bienenfeld - Westchester CC • Ralph Bertelle – Columbia Greene CC • Jack Narayan – SUNY Oswego • Michael Oppedism – Onondaga CC • Robert Rogers – SUNY Fredonia • Malcomb Sherman– SUNY Albany • William Thistleton – SUNY IT

9. Procedures Used In Creating a Rubric • Determine the standard to be assessed. • Write learning objectives for that standard. • Determine the style and scale that will be used. • Describe criteria for the highest and the lowest levels • Describe the criteria for the levels in between the highest and lowest.

10. Our rubric After much discussion, the panel decided that we will have a matrix with 2 columns and 4 rows. The rows will represent the levels of assessment. They are: • 3: Exemplary • 2: Generally Correct • 1: Partially Correct • 0: Incorrect

11. The panel decided to rate the student’s response with respect to the following criteria: • Does the student understand the problem? • Does the student use a clearly developed logical plan to solve the problem and is that plan evident in the solution? • Is the solution totally correct?

12. Learning Outcome #1 • Standard: Students will demonstrate the ability to interpret and draw inferences from mathematical models such as formulas, graphs, tables and schematics . • Learning Objectives: Given a mathematical model, the student will be able to: • Interpret the information • Draw inferences from that model

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15. Learning Outcome #2 • Standard: Students will demonstrate the ability to represent mathematical information symbolically, visually, numerically and verbally . • Learning Objectives: Given mathematical information, the student will be able to: • Represent that information symbolically • Represent that information visually • Represent that information numerically • Represent that information verbally

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20. Learning Outcome #3 • Standard: Students will demonstrate the ability to employ quantitative methods such as, arithmetic, algebra, geometry, or statistics to solve problems . • Learning Objectives: Given a problem, the student will be able to • Identify the appropriate quantitative method(s) necessary to solve that problem. • Use those methods to correctly solve that problem.

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23. Learning Outcome #4 • Standard: Students will demonstrate the ability to estimate and check mathematical results for reasonableness . • Learning Objectives: Given a mathematical problem, the student will be able to: • Estimate the result of that problem • Determine and justify the reasonableness of that result given the constraints of the problem.

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26. Learning Outcome #5 • Standard: Students will demonstrate the ability to recognize the limits of mathematical and statistical methods . • Learning Objectives: Given mathematical method, the student will be able to identify and articulate the limits of that mathematical method.

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29. An example… • Suppose that you invest $500.00 in an account and that interest is compounded continuously according to the formula • 1. If your annual rate of return is 4%, • a.How much money will you have at the end of 10 years? • b.How long will it take your money to double? • 2. What rate of return do you need in order for your money to double every 5 years?

30. Level 3:The student writes: .Substituting correctly for t demonstrates that the student understands how to use the model to answer the question.The student writes: .Substituting correctly for P and r demonstrates that the student is able to interpret the significance of those variables given in the model .The student writes: The balance in the account at the end of 10 years is $745.91.This is a complete and accurate answer.

31. Level 2:The student writes: .Substituting correctly for P and r demonstrates that the student is able to interpret the significance of those variables given in the model .The student writes: .Substituting correctly for t demonstrates that the student understands how to use the model to answer the question.The student writes: The balance in the account at the end of 10 years is $5204.05.This is a computational error involving order of operations. It is not unusual for a student not to question a result like this.

32. Level 1:The student writes: .Substituting incorrectly for P or r demonstrates that the student has some misunderstanding of how the model relates to the situation.The student writes: .The student attempts to use the model to answer the question.The student writes: The balance in the account at the end of 10 years is 1.1769E20.This is the calculator display, which is meaningless in this situation.

33. Level 0:The question is left blank or whatever is written is meaningless.

34. Questions and Answers • Do campuses have to assess all of their courses? • What do they do in cases where some of the learning outcomes are not covered in the courses? • Can I write my own assessment? • Can the same rubric be used for all courses?

35. Questions and Answers • Is there money for folks at campuses to construct the rubrics? • What are the learning outcomes? • How were the learning outcomes created? • What is a rubric? • What is a standard? • Are mathematicians using rubrics? • Is there a rubric for each learning outcome? • Does a campus have to use the same exam for all courses?

36. Questions and Answers • Can a campus use pre- and post-tests? • What happens to the data when the system gets it? • Can reporters access the data? • What is the process for a campus to get its assessment plan approved by GEAR? What is the time line? • How are testing and assessment related?