teaching to the “big ideas”: moving beyond the standards terry p. vendlinski ucla graduate...
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Teaching to the “Big Ideas”: Moving beyond the standards
Terry P. Vendlinski
UCLA Graduate School of Education & Information StudiesNational Center for Research on Evaluation,Standards, and Student Testing (CRESST)
Annual CRESST Conference
September 8, 2005
Overview
• Strengths and weaknesses of teaching to standards
• Integration of cognitive science and educational assessment research
• Ontological schema and Bayesian networks
Strengths and Weaknesses
• Improving instruction and learning by linking to standards (NCLB)
• Instruction needs to be focused but…. Organization and Sequence may be lacking
• Regular monitoring of student progress AND feedback about progress may be lacking
Example of Instruction
ei + 1 = 0
Assessment
ei + 1 =
Answer
ei + 1 = 0
What Would You Have to Learn in Order for This to Be Useful?
What do the symbols mean? What is this equation about?
What can you do with it? How can you use it?
What’s important about it?
Why has it been called the most beautiful equation in all of mathematics?
Someone who can answer these questions understands the meaning of what they’ve learned.
Niemi, 2005
The integration of cognitive science and educational assessment research
Our model of how students learn affects our assessment practice and our inferences (KWSK)
These, in turn, affect our instruction
Cognitive Science
Humans look for organizing features
We try to apply prior knowledge
The individual constructs meaning and understanding
Expert Knowledge Structure
Advanced Novice Knowledge Structure
CRESST Models
Determine the cognitive demand required to master a task or concept
Place the task or concept in context
Measure that against what is expected
Inverses
Additive
Laws of Arithmetic
Expression
Attaching NCTM Standards to the Ontology
•Recognize and use inverse properties (6 – 8)
•Use properties of zero.. in operations (4 – 5)
•Understand and use inverse relationships … within the operations of addition and subtraction ( 6 – 8)
Inverses
Additive
Laws of Arithmetic
Expression
Attaching California Standards to the Ontology
•Simplify numerical expressions by applying …
inverse (7)
•Use the inverse relationship between addition and subtraction (1 & 2)
Inverses
Additive
Laws of Arithmetic
Expression
Attaching Items to the Ontology
This is how a student did the problem 2 – (-7). If the student asked you to make sure it was correct, what would you say?
Give an explanation WHY you think each step is either correct
or incorrect:
2 – (-7)
2 + 7 + (-7) – (-7)
2 + 7
9
Inverses
Additive
Laws of Arithmetic
Expression
Using student work to infer understanding
Given:
2 – (-7)
Explain the step:
2 + 7 + (-7) – (-7)
This is correct since 7 + (-7) is zero and you don’t change anything by adding zero
Inverses
Additive
Laws of Arithmetic
Expression
Using student work to infer understanding
Given:
2 – (-7)
Explain the step:
2 + 7 + (-7) – (-7)
This is correct because (-7) – (-7) cancel each other out
making it 2 + 7 + 0
Inverses
Additive
Laws of Arithmetic
Expression
Using student work to infer understanding
Given:
2 – (-7)
Explain the step:
2 + 7 + (-7) – (-7)
This is incorrect because the 7 in 2 + 7 should be a -7
Number line
Bayesian Inference
The probability of event 1 GIVEN that event 2 has occurred is the product of the probability of event 2 given the probability of event 1 and the probability of event 1 divided by the probability of event 2
Bayesian Inference II
The probability that a student understands GIVEN that they’ve passed a test is the product of the probability that they pass a test given they understand and the general probability of understanding divided by the probability that students pass the test
Using the Ontology
Bayesian Ontologies
We can…
probabilistically infer student understanding
select assessments that are likely to be most informative
see new ways to organize instruction
