This document discusses different forms of assessment in mathematics education. It begins by defining the DepEd taxonomy of knowledge, process, understanding and product/performance. It then provides examples of mathematics skills and asks the reader to determine which category each one falls into. The document then discusses performance-based assessment and alternative forms such as portfolios. It provides characteristics of performance tasks and guidelines for constructing rubrics. Overall, the document aims to distinguish different types of assessment and provide information about designing performance-based tasks and rubrics.

1. ASSESSING PROCESS AND PRODUCTS:
MATHEMATICS SKILLS
Dr. Carlo Magno
Associate Professor of Educational Psychology
De La Salle University, Manila

2. DEPED TAXONOMY
• real-life application
of understanding
• enduring big ideas,
principles, and
generalizations inherent
to the discipline
• cognitive
operations that
the student
performs
• content of the
curriculum, the
facts and
information that
the student
acquires Knowledge Process
Product/PerformanceUnderstanding

3. DETERMINE WHETHER: KNOWLEDGE, PROCESS,
UNDERSTANDING, PRODUCT/PERFORMANCE
1. Students will describe quadratic function using
graphs.
2. Solves quadratic equation by completing squares.
3. Solves problems involving quadratic equation.
4. Identify expressions with radicals
5. Prove the theorem on angle similarity using SAS
similarity theorem.
6. Draw two objects to differentiate triangle similarity
and triangle congruence.
7. Prove the theorem on a 5X5 square.

4. 7. Determine the trigonometric ratio of special
triangles
8. Creates a graph of an arithmetic sequence.
9. Give examples of polynomial functions
10. Draw a circle and illustrate 5 different chords.
DETERMINE WHETHER: KNOWLEDGE, PROCESS,
UNDERSTANDING, PRODUCT/PERFORMANCE

5. DETERMINE WHETHER: KNOWLEDGE, PROCESS,
UNDERSTANDING, PRODUCT/PERFORMANCE

6. DETERMINE WHETHER: KNOWLEDGE, PROCESS,
UNDERSTANDING, PRODUCT/PERFORMANCE

7. DETERMINE WHETHER: KNOWLEDGE, PROCESS,
UNDERSTANDING, PRODUCT/PERFORMANCE

8. DETERMINE WHETHER: KNOWLEDGE, PROCESS,
UNDERSTANDING, PRODUCT/PERFORMANCE

9. DETERMINE WHETHER: KNOWLEDGE, PROCESS,
UNDERSTANDING, PRODUCT/PERFORMANCE

10. DETERMINE WHETHER: KNOWLEDGE, PROCESS,
UNDERSTANDING, PRODUCT/PERFORMANCE

11. ASSESSMENT COMPETENCIES FOR
TEACHERS
 Constructed by the AFT, NCME, NEA:
 Teachers should be skilled in:
1. choosing assessment methods appropriate
for instructional decisions.
2. Administering, scoring, and interpreting the
results of both externally produced and
teacher produced assessment methods.
3. Using assessment results when making
decisions about individual students,
planning teaching, and developing
curriculum and school improvement.
American Federation of Teachers, National Council on Measurement and Evaluation,
and National Education Association in the United States of America.

12. ASSESSMENT COMPETENCIES FOR
TEACHERS
4. Developing valid pupil grading procedures that
use pupil assessment.
5. Communicating assessment results to students,
parents, other lay audiences, and other
educators.
6. Recognizing unethical, illegal, and otherwise
inappropriate assessment methods and uses of
assessment information.

13. SHIFTS IN ASSESSMENT
 Testing Alternative assessment
 Paper and pencil Performance assessment
 Multiple choice Supply
 Single correct answer Many correct answer
 Summative Formative
 Outcome only Process and Outcome
 Skill focused Task-based
 Isolated facts Application of knowledge
 Decontextualized task Contextualized task

14. ALTERNATIVE FORMS OF ASSESSMENT
 Performance based assessment
 Authentic assessment
 Portfolio assessment

15. OBJECTIVES
 1. Distinguish performance-based
assessment with the traditional paper and
pencil tests.
 2. Construct tasks that are performance
based.
 Design a rubric to assess a performance
based task

16. TERMS
 Authentic
assessment
 Direct assessment
 Alternative
assessment
 Performance testing
 Performance
assessment
 Changes are taking
place in assessment

17. METHOD
 Assessment should measure what is really
important in the curriculum.
 Assessment should look more like instructional
activities than like tests.
 Educational assessment should approximate the
learning tasks of interest, so that, when students
practice for the assessment, some useful learning
takes place.

18. WHAT IS PERFORMANCE ASSESSMENT?
 Testing that requires a student to create an answer
or a product that demonstrates his/her knowledge
or skills (Rudner & Boston, 1991).

19. FEATURES OF PERFORMANCE ASSESSMENT
 Intended to assess what it is that students know
and can do with the emphasis on doing.
 Have a high degree of realism about them.
 Involve: (a) activities for which there is no correct
answer, (b) assessing groups rather than
individuals, (c) testing that would continue over an
extended period of time, (d) self-evaluation of
performances.
 Likely use open-ended tasks aimed at assessing
higher level cognitive skills.

22. PUSH ON PERFORMANCE ASSESSMENT
 Bring testing methods more in line with instruction.
 Assessment should approximate closely what it is
students should know and be able to do.

23. EMPHASIS OF PERFORMANCE ASSESSMENT
 Should assess higher level cognitive skills rather
than narrow and lower level discreet skills.
 Direct measures of skills of interest.

24. CHARACTERISTICS OF PERFORMANCE-BASED
ASSESSMENT
 Students perform, create, construct, produce, or do
something.
 Deep understanding and/or reasoning skills are needed and
assessed.
 Involves sustained work, often days and weeks.
 Calls on students to explain, justify, and defend.
 Performance is directly observable.
 Involves engaging in ideas of importance and substance.
 Relies on trained assessor’s judgments for scoring
 Multiple criteria and standards are prespecified and public
 There is no single correct answer.
 If authentic, the performance is grounded in real world
contexts and constraints.

25. VARIATION OF AUTHENTICITY
Relatively authentic Somewhat authentic Authentic
Indicate which parts of
a garden design are
accurate
Design a garden Create a garden
Write a paper on
zoning
Write a proposal to
change fictitious
zoning laws
Write a proposal to
present to city council
to change zoning laws
Explain what would
you teach to students
learning basketball
Show how to perform
basketball skills in
practice
Play a basketball
game.

26. CONSTRUCTING PERFORMANCE BASED
TASKS
1. Identify the performance task in which students
will be engaged
2. Develop descriptions of the task and the context in
which the performance is to be conducted.
3. Write the specific question, prompt, or problem
that the student will receive.
• Structure: Individual or group?
• Content: Specific or integrated?
• Complexity: Restricted or extended?

27. COMPLEXITY OF TASK
 Restricted-type task
 Narrowly defined and require brief responses
 Task is structured and specific
 Ex:
 Construct a bar graph from data provided
 Demonstrate a shorter conversation in French about what is
on a menu
 Read an article from the newspaper and answer questions
 Flip a coin ten times. Predict what the next ten flips of the coin
will be, and explain why.
 Listen to the evening news on television and explain if you
believe the stories are biased.
 Construct a circle, square, and triangle from provided materials
that have the same circumference.

28.  Extended-type task
 Complex, elaborate, and time-consuming.
 Often include collaborative work with small group of
students.
 Requires the use of a variety of information
 Examples:
 Design a playhouse and estimate cost of materials and labor
 Plan a trip to another country: Include the budget and itinerary,
and justify why you want to visit certain places
 Conduct a historical reenactment (e. g. impeachment trial of
ERAP)
 Diagnose and repair a car problem
 Design an advertising campaign for a new or existing product

29. IDENTIFYING PERFORMANCE TASK
DESCRIPTION
 Prepare a task description
 Listing of specifications to ensure that essential if
criteria are met
 Includes the ff.:
 Content and skill targets to be assessed
 Description of student activities
 Group or individual
 Help allowed
 Resources needed
 Teacher role
 Administrative process
 Scoring procedures

30. PERFORMANCE-BASED TASK QUESTION
PROMPT
 Task prompts and questions will be based on the
task descriptions.
 Clearly identifies the outcomes, outlines what the
students are encourage dot do, explains criteria for
judgment.

31. EXAMPLE OF A TASK PROMPT:

39. PERFORMANCE CRITERIA
 What you look for in student responses to evaluate
their progress toward meeting the learning target.
 Dimensions of traits in performance that are used to
illustrate understanding, reasoning, and proficiency.
 Start with identifying the most important dimensions
of the performance
 What distinguishes an adequate to an inadequate
demonstration of the target?

40. EXAMPLE OF CRITERIA
 Learning target:
 Students will be able to write a persuasive paper to
encourage the reader to accept a specific course of
action or point of view.
 Criteria:
 Appropriateness of language for the audience
 Plausibility and relevance of supporting arguments.
 Level of detail presented
 Evidence of creative, innovative thinking
 Clarity of expression
 Organization of ideas

41.  Watch video of Cody Green

42. RATING SCALES
 Indicate the degree to which a particular dimension
is present.
 Three kinds: Numerical, qualitative, combined
qualitative/quantitative

43.  Numerical Scale
 Numbers of a continuum to indicate different level of
proficiency in terms of frequency or quality
Example:
No Understanding 1 2 3 4 5 Complete
understanding
No organization 1 2 3 4 5 Clear organization
Emergent reader 1 2 3 4 5 Fluent reader

44.  Qualitative scale
 Uses verbal descriptions to indicate student
performance.
 Provides a way to check the whether each dimension
was evidenced.
 Type A: Indicate different gradations of the dimension
 Type B: Checklist

45.  Example of Type A:
 Minimal, partial, complete
 Never, seldom, occasionally, frequently, always
 Consistent, sporadically, rarely
 None, some, complete
 Novice, intermediate, advance, superior
 Inadequate, needs improvement, good excellent
 Excellent, proficient, needs improvement
 Absent, developing, adequate, fully developed
 Limited, partial, thorough
 Emerging, developing, achieving
 Not there yet, shows growth, proficient
 Excellent, good, fair, poor

46.  Example of Type A: Checklist

47.  Holistic scale
 The category of the scale contains several criteria,
yielding a single score that gives an overall impression
or rating
Example
level 4: Sophisticated understanding of text
indicated with constructed meaning
level 3: Solid understanding of text indicated with
some constructed meaning
level 2: Partial understanding of text indicated with
tenuous constructed meaning
level 1: superficial understanding of text with little or
no constructed meaning

48. EXAMPLE HOLISTIC SCALE

49.  Analytic Scale
 One in which each criterion receives a separate score.
Example
Criteria Outstanding
5 4
Competent
3
Marginal
2 1
Creative ideas
Logical organization
Relevance of detail
Variety in words and
sentences
Vivid images

50. RUBRICS
 When scoring criteria are combined with a rating scale,
a complete scoring guideline is produced or rubric.
 A scoring guide that uses criteria to differentiate
between levels of student proficiency.

51. EXAMPLE OF A RUBRIC

52. GUIDELINES IN CREATING A RUBRIC
1. Be sure the criteria focus on important aspects of
the performance
2. Match the type of rating with the purpose of the
assessment
3. The descriptions of the criteria should be directly
observable
4. The criteria should be written so that students,
parents, and others understand them.
5. The characteristics and traits used in the scale
should be clearly and specifically defined.
6. Take appropriate steps to minimize scoring frame

53. WORKSHOP
 Create a performance based task.
 Indicate the following:
 Nature of the final product
 What students are suppose to do
 Criteria for the marking
 Group 1: Theorems of proportionality
 Group 2: Trigonometric ratio
 Group 3: Rational Expression
 Group 4: Quadratic function

54. PORTFOLIO ASSESSMENT: EXPLORATION
 Have you ever done a portfolio?
 Tell me about this experience. Did you
enjoy it?
 What elements did you include in your
portfolio?
 Are the materials placed in the portfolio
required?
 Watch video on Portfolio

55. WHAT ARE PORTFOLIOS?
 Purposeful, systematic process of collecting and
evaluating student products to document progress
toward the attainment of learning targets or show
evidence that a learning target has been achieved.
 Includes student participation in the selection and
student self-reflection.
 “A collection of artifacts accompanied by a reflective
narrative that not only helps the learner to
understand and extend learning, but invites the
reader of the portfolio to gain insight about learning
and the learner (Porter & Cleland, 1995)

56. CHARACTERISTICS OF PORTFOLIO
ASSESSMENT
 Clearly defined purpose and learning targets
 Systematic and organized collection of student
products
 Preestablished guidelines for what will be included
 Student selection of some works that will be
included
 Student self-reflection and self-evaluation
 Progress documented with specific products and/or
evaluations
 Portfolio conferences between students and
teachers

57. PURPOSE OF PORTFOLIO
 Showcase portfolio: Selection of best works. Student
chooses work, profile are accomplishments and
individual profile emerges.
 Documentation portfolio: Like a scrapbook of
information and examples. Includes observations, tests,
checklists, and rating scales.
 Evaluation portfolio: More standardized. Assess
student learning with self-reflection. Examples are
selected by teachers and predetermined.

58. ADVANTAGES OF PORTFOLIO
 Students are actively involved in self-evaluation and
self-reflection
 Involves collaborative assessment
 Ongoing process where students demonstrate
performance, evaluate , revise , and produce quality
work.
 Focus on self-improvement rather than comparison with
others
 Students become more engaged in learning because
both instruction and assessment shift from teacher
controlled to mix of internal and external control.
 Products help teachers diagnose learning difficulties
 clarify reasons for evaluation
 Flexible

59.  Final Workshop
 crlmgn@yahoo.com