Standards and Rubrics for Assessing Learning Outcomes in Mathematics

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## Standards and Rubrics for Assessing Learning Outcomes in Mathematics

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**Standards and Rubrics for Assessing Learning Outcomes in**Mathematics GEAR Conference April 27th – 28th**Presenters:Maryann Faller – Adirondack CCRalph Bertelle**– Columbia-Greene CCJack Narayan – SUNY Oswego**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.**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**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.**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.**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.**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**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.**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**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?**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**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**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.**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.**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.**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?**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.**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.**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.**Level 0:The question is left blank or whatever is written is**meaningless.**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?**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?**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?