Designing Effective Learning Outcomes in Mathematics

1. How to Prepare Learning Outcomes Department of Mathematics

2. Definition of Learning Outcomes • Learning outcomes are statements of what is expected that a student will be able to do as a result of a learning activity and can reliably demonstrate at the end of a course or program. • Expected learning outcomes should not describe educational experiences, but rather the important knowledge, abilities or values these experiences enable students to possess, not merely things that are easily achieved or measured. • Learning outcomes refer to observable and measurableknowledge, skills, and attitudes.

3. One should create a reasonably complete list of the significant outcomes of the course. • Each major course topic may have 1-3 learning outcomes. • Although some students will learn more than others, owing to their ability and level of effort, expected learning outcomes should describe areas of knowledge and skill that apply to all conscientious students. • In practice less than 100% of students completing a program of study or course may achieve a given learning outcome, but we aim to have all students do so.

4. Learning Outcomes written at the course level should: • state clear expectations - learners know what they have to do to demonstrate that they have achieved the learning outcomes; • reflect essential knowledge, skills or attitudes; • be general enough to capture important learning, but specific enough to allow for a fair assessment, whose criteria are clearly communicated to students; • focus on results of the learning experiences; • reflect the desired end of the learning experience, not the means or the process; • preferably state only one performance per outcome; • represent the minimal acceptable level of performance that a student needs to demonstrate in order to be considered successful; • as much as possible, be written in intelligible language, understandable to students.

5. Steps in writing Learning Outcomes • identify the major topics of a course; • classify the outcome focusing on student actions; • identify the level of learning required from the student; • consider how you will assess the achievement of the outcome; • consider success criteria; • choose a specific action verb for each outcome.

6. Learning Outcome statements may be broken down into three main components • the criterion or standard for acceptable performance; • an action word thatidentifies the performance to be demonstrated; • a learning statement that specifies what learning will be demonstrated in the performance;

7. Each outcome begins with the phrase: “The student will be able to…” or something like that, followed by an action verb. • Some common action verbs that may be included in learning outcomes to specify six different sorts of outcome

8. Student recalls or recognizes information, ideas, and principles which were learned. Knowledge: Arrange, cite, define, enumerate, identify, list, match, memorize, name, recall, recognize, relate,repeat, reproduce, select, state. Student recalls or recognizes information, ideas, and principles which were learned.

9. Comprehension: Classify, cite, convert, describe, discuss, estimate, explain, express, generalize, give examples, identify, indicate, locate, recognize, report, restate, review, select, paraphrase, summarize, translate Student translates, comprehends, or interprets information based on prior learning.

10. Application: Apply, chart, choose, compute, construct, control, determine, demonstrate, develop, employ, establish, extend, illustrate, implement, inform, instruct, interpret, operate, practice, predict, prepare, produce, project, provide, relate, report, schedule, show, sketch, solve,transfer, use, utilize, write. Student selects, transfers, and uses data and principles to complete a problem or task with a minimum of directions

11. Analysis: Student distinguishes, classifies, and relates the assumption, hypotheses, evidence, or structure of a communication or concept. • Analyze, break down, calculate, categorize, compare, contrast, correlate, criticize, diagram, differentiate, discriminate, • distinguish,examine, experiment,illustrate, • infer,outline,pointout, prioritize, • question,recognize, • separate, subdivide, test.

12. Synthesis: Adapt, anticipate, arrange, assemble, categorize, collaborate, collect, combine, communicate, compare, complete, compose, construct, contract, contrast, create, design, devise, express, facilitate,formulate, generate, incorporate, individualize, initiate, integrate, model, organize, plan, prepare, propose, rearrange, reconstruct, reorganize, revise, set up, structure, substitute, validate, write Student originates, integrates, and combines ideas into a product, plan, or proposalthat is new to him or her.

13. Evaluation: Appraise, argue, assess, attach, choose, compare, conclude, confront, criticize, decide, defend, estimate, interpret, judge, justify, predict, rate, reframe, score, select, support, value, evaluate. Student appraises, assesses, or criticizes something on the basis of specific standards and criteria.

14. Mathematics Learning Outcomes • Aims are the broad intentions and orientation of the course or programof study, i.e. what the instructor plans to do for the students and how. • Intended learning outcomes carry a more specific meaning. • They describe what the students should be able to do or demonstrate, in terms of particular knowledge, skills and attitudes, by the end of the course.

15. Theexample of possible aims for the service mathematical course can be: • for the students to become comfortable with manipulation of simple mathematical objects (using paper and pencil or technology as appropriate), • to give the background needed by the students to continue their studies in statistics, finance, business and other application fields, • for the students to develop skill in quantitative reasoning by examining how appropriate mathematical techniques can be used to analyze questions from many different areas.

16. The examples of possible learning outcomes for the service mathematical course can be: 1. Perform basic arithmetic operations. 2. Determine and interpret percents. 3. Convert units of measurement using proportions. 4. Solve introductory linear equations. 5. Solve application problems using formulas. 6. Solve algebraic equations and inequalities. 7. Examine and interpret the graphs of algebraic functions. 8. Solve systems of equations. 9. Solve application problems using algebraic functions.

17. 10. Use modeling graphs to interpret and make predictions about real-world functions. 11. Translate verbally stated problems into appropriate mathematical forms. 12. Demonstrate the concept of a limit from graphical and computational perspectives. 13. Derive the derivative of a function algebraically from the limit definition of a derivative. 14. Recognize the derivative as a rate of change. 15. Compute derivatives b1y the differentiation rules. 16. Describe the relationships between position, velocity, and acceleration. 17. Use derivatives to compute linear approximations to functions. 18. Use calculus to solve problems involving indeterminate forms of limits.

18. 19. Use the relationship between the graph of a function and its derivatives to solveproblems involving analytic geometry and optimization. 20. Demonstrate an understanding of the Mean Value Theorem and the Fundamental Theorem of Calculus. 21. Demonstrate an understanding of the definition of a Riemann integral. 21. Demonstrate an understanding of the definition of a Riemann integral. 22. Compute integrals by basic rules.