PERCENTILE

What is percentile?

Percentile (or Centile)

the value of a variable below which a certain percent of observations fall.

Nearest Rank

One definition of percentile, often given in texts, is that the P-th percentile ( ) of N ordered values (arranged from least to greatest) is obtained by first calculating the (ordinal) rank

rounding the result to the nearest integer, and then taking the value that corresponds to that rank.

Linear interpolation

Linear interpolation between closest ranks

An alternative to rounding used in many applications is to use linear interpolation between the two nearest ranks.

In particular, given the N sorted values  , we define

the percent rank corresponding to the nth value as:

.

Weighted Percentile

Suppose we have positive weights    associated, respectively, with our N sorted sample values. Let

,

the  n-th partial sum of the weights. Then the formulas above are generalized by taking

and .

AssessmentWhat Is Assessment as Learning?

Assessment as learning • focuses on students and emphasizes assessment as a

process of metacognition (knowledge of one’s own thought processes) for students.

• emerges from the idea that learning is not just a matter of transferring ideas from someone who is knowledgeable to someone who is not, but is an active process of cognitive restructuring that occurs when individuals interact with new ideas.

• students are the critical connectors between assessment and learning.

• For students to be actively engaged in creating their own understanding, they must learn to be critical assessors who make sense of information, relate it to prior knowledge, and use it for new learning.

Assessment

What Is Assessment as Learning?

Assessment as learning:• regulatory process in metacognition; that is, students

become adept at personally monitoring what they are learning, and use what they discover from the monitoring to make adjustments, adaptations, and even major changes in their thinking.

• based in research about how learning happens, and is characterized by students reflecting on their own learning and making adjustments so that they achieve deeper understanding.

AssessmentThe teacher’s role in promoting the development of

independent learners through assessment as learning is to:

• model and teach the skills of self-assessment• guide students in setting goals, and monitoring their

progress toward them• provide exemplars and models of good practice and

quality work that reflect curriculum outcomes• work with students to develop clear criteria of good

practice

AssessmentThe teacher’s role in promoting the development of

independent learners through assessment as learning is to:

• guide students in developing internal feedback or self-monitoring mechanisms to validate and question their own thinking, and to become comfortable with the ambiguity and uncertainty that is inevitable in learning anything new

• provide regular and challenging opportunities to practice, so that students can become confident, competent self-assessors

• monitor students’ metacognitive processes as well as their learning, and provide descriptive feedback

• create an environment where it is safe for students to take chances and where support is readily available

Current Views of AssessmentAssessment serves many purpose.

• Conventional assessment• Alternative assessment• Authentic assessment

Instruction and assessment should merge.

Assessment that corresponds with instruction should relate to student’s prior knowledge, use complete text passages, accept different interpretations, and allow the reader to vary reading strategies.

Current Views of AssessmentAlternative assessment should be based on the following

principles:

1. The major purpose of assessment is improvement of students learning.

2. Assessment is fair and equitable for all students.

3. Assessment involves all members of the educational community.

4. Communication about assessment is clear and regular.

5. Assessment includes a variety of perspectives and data.

6. Professional collaboration supports assessment.

7. Activities assessed are meaningful and contextualized.

8. Assessment is continuous.

What type of assessment do we have?

Formal assessment

VS

Alternative assessment Authentic assessment

Alternative Assessment Refers to all types of assessment other than formal,

standardized tests.Observation strategies• Observation, interaction, and analysis• Kidwatching (Yetta Goodman, 1978)• Anecdotal records• Checklists and Rating scales• Rubrics• Conferences and Interviews• RetellingsAppraising InterestsPortfolio AssessmentSelf-AppraisalInformal Tests

Authentic Assessment

The aim of authentic assessment is to assess many different kinds

of literacy abilities in contexts that closely resemble the actual

situations in which those abilities are used.

Authentic Assessment 1. Connecting, Reflecting, and Feedback (Aspects of Authentic

Assessment)Metacognitive strategies

• Mrs. Potter’s Questions: What were you expect to do in this assignment? What did you do well? If you had to do this task over, what would you do differently? What help do you need from me?

• KWL strategy• PMI strategy• Transfer journals• Wrap-around• Reflection page• Learning logs• Seesaw thinking• Pie in the face• Stem sentences

2. Self Assessment (Dimension of Assessment)

What do we need in assessment?

Formal assessment tools

VS

Alternative assessment and Authentic assessment tools

Authentic Assessment Tools

• Graphic Organizers and Concept Mapping

• Performance Products• Live Performances and

Presentations• Rubrics• Learning Logs and Journals• Projects• Portfolios