assessment and evaluation in the mathematics classroom
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Assessment and Evaluation in the Mathematics Classroom. Jane Silva Instructional Leader K-8. Objectives. > To examine the principles of effective assessment > To examine how to collect and interpret assessment data. - PowerPoint PPT PresentationTRANSCRIPT
Assessment and Evaluationin the
Mathematics Classroom
Jane SilvaInstructional Leader K-8
Objectives
> To examine the principles of effective assessment
> To examine how to collect and interpret assessment data
“From their earliest school experience, students draw life-shaping conclusions about themselves as learners on the basis of the information provided to them as a result of classroom assessments.”
- Stiggins, Student-Involved Classroom Assessment, Prentice-Hall, 2001, p.48.
Recall your own assessment experiences as students.
Recall your own assessment experiences as students.
What kind of meaningful classroom assessment information do we want to provide to our students?
Select Expectations
Summative/ Diagnostic culminating Assessment assessment and evaluation Adapt program Select and based on implement formative learning assessments experiences
Ongoing, formative assessments (with feedback to students)
THE TEACHING/ LEARNING
CYCLE
Types of AssessmentDiagnostic Assessment:
Assessment FOR Learning
Formative Assessment:Assessment FOR Learning
Summative Assessment:Assessment OF Learning
Assessment AS Learning
Types of AssessmentDiagnostic Assessment:
Assessment FOR Learning
Formative Assessment:Assessment FOR Learning
Summative Assessment:Assessment OF Learning
Assessment AS Learning
Knowing what ingredients you already have and those that are still needed to make excellent soup, that’s diagnostic;
When the cook tastes the soup, that’s formative;
When the guests taste the soup, that’s summative.
When they think it’s good or bad that’s evaluation.
Recipe for Assessment
Why Do We Assess?
We Assess To document student and teacher progress To provide feedback to the student and
family, and the teacher To inform instructional decisions
Wormelli, R. (2006). Fair Isn’t Always Equal
We do not Assess To motivate students To punish students To sort students
Wormelli, R. (2006). Fair Isn’t Always Equal
Ten Approaches to Avoid in Assessment and Grading
Ten Approaches to Avoid in Assessment and Grading
1. Incorporating nonacademic factors, such as effort, behaviour, and attendance
It is agreed that there is a high correlation between academic success and effort, behaviour and attendance.
However, we don’t have a commonly accepted, legally justifiable, non-subjective method for measuring effort.
Instead, specific feedback on these factors should be communicated to students.
Ten Approaches to Avoid in Assessment and Grading
2. Penalizing students’ multiple attempts at mastery
“Feedback that is given on an assignment that can’t be revised or that is not clearly and specifically related to future work is unlikely to be seen as useful by the student…(s)he can’t hope for a slight improvement in the grade, despite the fact that he now understands how to do the work.” (Nolen & Taylor, 2005, p.60)
Ten Approaches to Avoid in Assessment and Grading
3. Grading Practice (bad homework)
Confabulation When the mind seeks the big-picture
connections of something that is learned, and when it doesn’t find all the pieces of the puzzle, it makes up information or borrows from other memories and inserts false information into holes of missing information. Successful teachers don’t give homework unless their students have already mastered the concepts.” p.116
Ten Approaches to Avoid in Assessment and Grading
4. Withholding assistance with the learning when it’s needed
Accommodations If providing glasses, for example,
allows students to follow and participate in lesson, why not allow this learning tool.
If providing a calculator, for example, allows students to identify and organize salient information that will allow them to be competitive with the best thinkers in the class, why not allow this learning tool.
Ten Approaches to Avoid in Assessment and Grading
5. Assessing students in ways that do not accurately indicate their mastery
Speed
Perseverance
Level of conformity
Mathematical Sophistication
Students Differ in Math via:
Ten Approaches to Avoid in Assessment and Grading
6. Allowing extra credit and bonus points
Assessment “of” or “for” learning?
“Teachers are applying assessment for learning when they plan to revisit a particular big idea later in the program if the concept is not as well understood as it should be.” LNS, P.50 Bonus assignments don’t necessary move students along the continuum.
Ten Approaches to Avoid in Assessment and Grading
7. Group grades
Learning Skills vs. Content Knowledge
Cooperative learning is an outstanding teaching strategy and technique used to teach students about a topic, not a demonstration of proficiency in that topic itself.
Ten Approaches to Avoid in Assessment and Grading
8. Grade on a curve
How Do We Grade?We must compare students to the standards and not to each other (grading on a curve).
Let’s use pilots to show why this is a good idea:
In a classroom where all students are above
standard”
Good students
“fail”
Meanwhile, across the hall in a classroom where all
students are “below standard”
Bad students “pass”
Ten Approaches to Avoid in Assessment and Grading
9. Using norm-referenced terms to describe criterion-referenced attributes
Avoid Norm-Referenced Grading
Shift in assessment practice away from comparing students’ performance with that of other students towards comparing students’ performance with established criteria.
Use Criterion-Referenced Grading
Grade students by comparing them to curriculum standards.
Consider the “Mountain Curve” where we try to move all students toward the standards.
Ten Approaches to Avoid in Assessment and Grading
10. Recording zeros for work not done
Why Do We Grade?Low grades push students farther from
our cause, they don’t motivate students.
High grades can have short-term effects on motivation as well, if it affects students’ intrinsic motivation.
Classroom Assessment & Grading that Work
Classroom Assessment & Grading that Work
The “grade” you often observe is a combination of the student’s “true
score” and an “error score”.
A “true score” represents a student’s actual level of achievement.
Classroom Assessment & Grading that Work
How can we find true score?
Classroom Assessment & Grading that Work
How can we find true score?
Consider the Item Response Theory (IRT)
- Uses complex mathematics to translate a students pattern of responses to a trait score on
that distribution- We use a scale that represents performance
along a continuum
For this theory to hold, our assessments must include Type I, II,
and III items.
To relate this to our practices, we may say that our assessments should include level 1, 2, 3, and 4
questions.
Let’s look at Type I, II, and III items.
Type I Items or Tasks
- Address the basic details and processes that are relatively easy for students
- Teacher asks: About this topic, what are the basic details and processes students should understand or be able to do fairly easily if they were paying attention in class?
Type I Items and Tasks for Information
- Vocabulary terms: a common type of basic detail
- Facts: identify characteristics of specific persons, places, living things, nonliving things, events and causes of events
- Time sequences: involve events that occurred between two points in time
Type I Items and Tasks for Mental Procedures
- Single rules: Ex. Capitalization – if the word begins a sentence, then capitalize the word
- Algorithms: procedures that do not vary much in their application once learned
- Tactics: may be used differently from one situation to another
Type II Items or Tasks
- Address more complex ideas and processes and are more difficult for students
- Teacher asks: About this topic, what are the more complex ideas and processes students should understand or be able to do if they were paying attention in class?
Type II Items and Tasks for Information
- Generalizations: statements for which examples can be provided; identify characteristics of classes of the same type of information
- Principals: deals with cause/effect relationships; geared toward predicting what will occur in a given situation
Type II Items and Tasks for Mental Procedures
- Decision making: process of generating and applying criteria to select from among seemingly equal alternatives
- Problem solving: process of overcoming constraints or limiting conditions that are in the way of pursuing goals
- Experimental inquiry: process of generating and texting explanations of observed phenomena
- Investigation: process of identifying and resolving issues that involve confusions or contradiction
- Invention: process of developing unique products or processes that fulfill perceived needs
Type II Items and Tasks
Constructed-Response Items:- Short written response- Essays (addresses a generalization)
Type III Items or Tasks
- Require students to make inferences or applications that go beyond what was taught in class
- Teacher asks: About this topic, what inferences and applications might students be able to make even though they go beyond what was taught in class?
Type II Items and Tasks for Information
Sometimes involves:- Comparing: identifying similarities and
differences- Classifying: grouping into categories based
on their like characteristics- Creating metaphors: identifying a general
pattern that connects information that is not related at the literal level
- Creating analogies: identifying the relationship between two sets of items
- Analyzing errors
Type III Items and Tasks for Mental Procedures
- Address the extent to which students can apply the procedure in a context not addressed in class
Type III Items and Tasks
Constructed-Response Items:- Short written response- Essays (go beyond expectations)
Sample AssessmentSection I:
1. Which company has the highest daily rate?2. Which company has the most free mileage?3. If each company had the same daily rate and the same amount
of free mileage, which would be cheapest?4. If each company had the same amount of free mileage and the
same cost per mile, which company would be the most expensive?
5. Once you’ve used up your free mileage, which company would cost the least amount of money to travel 100 miles in a single day?
Red Rental Easy Rental Reliable Rental
J&S Rental
Daily Rate $43.00 $27.50 $40.00 $35.25
Free Mileage
1 200 500 900 800
Cost per Mile
$0.22/mile $0.32/mile $0.25/mile $0.20/mile
Sample AssessmentSection II:
6. If you travel 100 miles per day, which company is the least expensive for5 days:10 days:15 days:20 days:Create a table or graph that shows how expensive each company is for each of the four options above (5 days, 10 days, 15 days, 20 days), and explain how you calculated your answers.
Red Rental Easy Rental Reliable Rental
J&S Rental
Daily Rate $43.00 $27.50 $40.00 $35.25
Free Mileage
1 200 500 900 800
Cost per Mile
$0.22/mile $0.32/mile $0.25/mile $0.20/mile
Sample AssessmentSection III:
7. Each of the four companies could be considered the “best deal” under certain conditions. For each company, describe the situation under which it would be the best selection. In your answer and explanation, use the daily rate, free mileage, and the rate per mile after free mileage.
Red Rental Easy Rental Reliable Rental
J&S Rental
Daily Rate $43.00 $27.50 $40.00 $35.25
Free Mileage
1 200 500 900 800
Cost per Mile
$0.22/mile $0.32/mile $0.25/mile $0.20/mile
How do you Grade this type of Assessment?
Use the scoring scale. A “+” indicates that the student was
successful with this type of question.
Quick Reference Guide for the Simplified Scoring Scale
Student Pattern of ResponsesType I Items
+ + + Some understanding with help
0 with help
Type II Items
+ + 0 Some understanding with help
0 with help
Type III Items
+ 0 0 0 with help
0 with help
Score 4.0 3.0 2.0 1.0 0.0
Quick Reference Guide for the Complete Scoring ScaleStudent Pattern of Responses
Type I Items
+ + + + + part part with help
part with help
0with help
Type II Items
+ + + part 0 0 part with help
0with help
0with help
Type III Items
+ part 0 0 0 0 0with help
0with help
0with help
Score 4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0
Quick Reference Guide for the Complete Scoring Scale
Score on Scale
Description of Place on Scale
4.0 In addition to Score 3.0 performance, in-depth inferences and applications that go beyond what was taught.
3.5 In addition to Score 3.0 performance, partial success at inferences and applications that go beyond what was taught.
3.0 No major errors or omissions regarding any of the information and/or processes (simple or complex) that were explicitly taught.
2.5 No major errors or omissions regarding the simpler details and processes and partial knowledge of the more complex ideas and processes.
2.0 No major errors or omissions regarding the simpler details and processes but major errors or omissions regarding the more complex ideas and processes.
1.5 Partial knowledge of the simpler details and processes but major errors or omissions regarding more complex ideas and processes.
1.0 With help, a partial understanding of some of the simpler details and processes and some of the more complex ideas and processes.
0.5 With help, a partial understanding of some of the simpler details and processes but not the more complex ideas and processes.
0.0 Even with help, no understanding or skill demonstrated
What to do if Students Responses Don’t Follow a
Logical Pattern- Realize that no assessment can ever provide perfectly accurate data about a student
- Drop some items because they are deemed to be invalid
- Rethink the classification of specific items
- Meeting individually with students