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### Assessing using the Rubric and the Power Law

Anchorage - October 9, 2009

What is Assessment?

- Anything a teacher does to gather information about a student’s level of knowledge regarding a specific topic

Obtrusive assessment

- Assessment directed/assigned by the teacher
- Instruction stops to administer assessment
- Assessment can take many forms; including tests, classroom activities, assignment, projects, presentations, interviews
- Scores on the assessment are taken and recorded

Unobtrusive

- Teacher observes a student performing skill or process, teacher could also use data recorded by students
- Better suited to skills and processes that can be observed
- Instruction does not stop in the classroom
- Also occurs outside of the classroom, any place the teacher can observe a student
- Scores can be recorded

Student Generated

- Student designs assessment to demonstrate status on topic
- Teacher records score and uses student demonstration as a piece of information
- Student friendly version of the rubric would be an important tool

Formative vs. summative

- Formative and summative assessments actually don’t exist!
- ANY assessment can be formative or summative –DEPENDING ON HOW THE DATA IS USED!
- Formative – scores taken during the course of learning to determine where a student is at that point in time
- Summative – a score taken and used to describe where a student is at the end of a course of learning

Three Uses of Assessment

- Formative Scores
- Summative Scores
- Instructional Feedback

Formative Scores

- Taking and recording scores on assessments to determine where a student is at a particular point in time
- Assessment can take any form
- Multiple formative scores can be used to develop a learning trend and ultimately develop a summative score
- Used to track student progress towards a learning goal

Summative Score

- A score taken and recorded to measure where a student ends up on a learning goal
- Typically used to determine and report a “grade”
- Assessment can take any form
- Should be used in conjunction with formative scores to determine summative score
- Use the “Power Law” or Learning trend to determine a summative score; NOT AN AVERAGE OF SCORES!

Power Law

Observed

Score

1

1

1.5

1.5

2

1.5

3

3

2.5

Learning Trend = 2.21

2.21

2.08

2

Average Score = 1.64

1.94

1.78

1.55

1.5

Mode = 1.5

1.24

1

.71

.5

0

Pre-Test Score 2 Score 3 Score 4 Score 5 Score 6 Post-Test

The Power law

- The power law can be applied to come up with a more accurate estimation of a student’s true score
- Power law estimations are typically far closer to a student’s observed score than averaged scores
- The power law is a mathematical function that takes into account the number of assessments, the score on each assessment and the time between assessments to calculate an estimated ‘true’ score
- y=atb where y is a score on a particular assessment, t is the time at which the assessment was administered and a and b are constants

How is the power law used?

- Electronic grade books can be designed to automatically calculate it
- Teachers can use their professional judgment by collecting data and looking for the pattern in the data. The data points will probably fit a power law curve over time.
- For example, a student (using the rubric), gets the following scores
- 0.0, 1.0, 2.0, 2.5, 2.5, 2.5, 3.0, 3.0, 3.5, 3.0
- What would the student’s estimated true score be?
- Averaging results in a score of 2.3 – the student is penalized for not knowing the information at the beginning

”

Using Teacher Judgment to Determine a student’s grade

- Imagine that a student has received the following scores on a measurement topic:
- 1.0, 1.0, 1.5, 1.5, 2.0, 1.5, 3.0
- What grade would they receive?
- In your professional judgment –
- Do they deserve a 3.0? Why or why not?
- Do they deserve a 2.0? Why or why not?
- Considerations: Look at the trend in the data – is it going up? Have they demonstrated consistent success at any level? Do you believe they can accomplish a specific level? Do you need more data?

How many data points do I need?

- The rubrics are designed so that a teacher can use fewer data points based on a set criteria to estimate the “true score”
- The short answer is that you need as many as it takes to get a good picture; using professional judgment, assessment data, and your knowledge of the student; of what a student knows at any given period of time
- 4- 5 are ideal. The less certain you are about a student’s “true score”, the more data you need

Implications

- Zeros given on an assignment or assessment because the student did not do it skew the calculation of a true score
- If you are trying to measure what a student knows and is able to do, use other means to measure and report work completion, behavior etc.
- A separate set of rubrics, or a separate grade can be used

Instructional Feedback

- Data from assessments used to determine and adjust course of instruction
- Represents a student’s or class’s understanding or progress towards a learning goal at any point in time
- Typically not recorded or scored

Designing Assessments - Obtrusive

- Assessments can be designed to assess all levels of the rubrics at the same time.
- Advantage – Students know what the ultimate goal is
- Disadvantage – Students begin a course of learning with very low scores, but improve from there
- Assessments could be designed to assess level 2.0 material first, and once mastered, move on the level 3.0
- Advantage – Opportunity for individualized instruction, foundational material mastered before moving onto learning goal
- Disadvantage – If used for a whole class, may hold students back that are ready to move on. Students may not have a clear picture of the ultimate goal

Designing assessments - unobtrusive

- Create situations that allow the teacher to observe student performing skills or processes
- “Catch” students performing the skill during the course of instruction
- Record data just like any other assignment

Designing assessments – Student generated

- Allow and encourage students to come up with their own way to demonstrate progress
- Record data and use to help determine progress
- Write a student friendly version of the rubric
- Place responsibility on students to provide data or “prove” their progress to teacher

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