Transcript Math Dept Presentation (23Jan2009)

How to Prepare
Learning Outcomes
Department of Mathematics
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
measurable knowledge, skills, and attitudes.
• 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.
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.
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.
Learning Outcome statements
may be broken down into three
main components
• the criterion or standard for acceptable
performance;
• an action word that identifies the
performance to be demonstrated;
• a learning statement that specifies what
learning will be demonstrated in the
performance;
• 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
Knowledge:
• Student recalls or
Student recalls or
recognizes
recognizes
information, ideas,
information, ideas,
and principles which
and principles which
were learned.
were learned.
Arrange, cite, define,
enumerate, identify, list,
match, memorize, name,
recall, recognize, relate,
repeat, reproduce, select,
state.
Comprehension:
Student translates,
comprehends, or
interprets information
based on prior
learning.
Classify, cite, convert,
describe, discuss,
estimate, explain, express,
generalize, give examples,
identify, indicate,
locate, recognize, report,
restate, review, select,
paraphrase, summarize,
translate
Application:
Student selects,
transfers, and uses
data and principles to
complete
a problem or task with
a minimum of
directions
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.
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, point out,
prioritize,
question, recognize,
separate, subdivide, test.
Synthesis:
Student originates,
integrates, and combines
ideas into a product, plan,
or proposal that is new to
him or her.
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
Evaluation:
Student appraises,
assesses, or criticizes
something on the basis of
specific standards and
criteria.
Appraise, argue, assess,
attach, choose, compare,
conclude, confront,
criticize, decide, defend,
estimate, interpret, judge,
justify, predict, rate,
reframe, score, select,
support, value, evaluate.
Mathematics Learning Outcomes
• Aims are the broad intentions and orientation of
the course or program of 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.
The example 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.
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.

9. Solve application problems using algebraic functions.
8. Solve systems of equations.
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.
19. Use the relationship between the graph of a function and its
derivatives to solve problems 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.