IEA Teacher Education Study in Mathematics

3rd NRC Meeting, June 25-29, 2007. Taipei, Chinese Taipei.

Michael C. Rodriguez

University of Minnesota & Michigan State University

Approaches to Data Analysis: Mathematics Content and Pedagogy

IEA Teacher Education Study in Mathematics

3rd NRC Meeting, June 25-29, 2007. Taipei, Chinese Taipei.

IEA Teacher Education Study in Mathematics

3rd NRC Meeting, June 25-29, 2007. Taipei, Chinese Taipei.

Scaling

Rasch Model Scaling A probabilistic model based on the interaction

of a person and an item. Slight philosophical difference between Rasch

measurement and IRT – one based on an analogy with the properties of physical measurement

IEA Teacher Education Study in Mathematics

3rd NRC Meeting, June 25-29, 2007. Taipei, Chinese Taipei.

From Numbers to Meaning

Numbers themselves do not mean much. Is 10 meters a short distance? Long distance?

We need context to bring meaning to the measure: 10 meters.

However, 10 meters should always be 10 meters, no matter who takes the measure or how it is taken.

IEA Teacher Education Study in Mathematics

3rd NRC Meeting, June 25-29, 2007. Taipei, Chinese Taipei.

Sample Dependent Statistics

Is an item with a p-value of .90 easy or difficult? …90% passed the item…

Is a person with a score of 5 out of 50 items low in ability? …correctly answered 10% of the items

IEA Teacher Education Study in Mathematics

3rd NRC Meeting, June 25-29, 2007. Taipei, Chinese Taipei.

Confucius: The First Sage Psychometrician?

John Linacre, International Symposium On Measurement & Evaluation (ISME), 2005

The requirement for good measurement for the regulation of society has been known for thousands of years. Here is Confucius:

jin quan liang

“Chau conferred great gifts, and the good were enriched. …He carefully (jin) attended to (quan) the weights and measures (liang), examined the body of the laws, restored the discarded officers, and the good government of the kingdom took its course.” (Confucius, The Analects, 20. ca. 500 BCE).

IEA Teacher Education Study in Mathematics

3rd NRC Meeting, June 25-29, 2007. Taipei, Chinese Taipei.

Rasch Scaling

Person-free item difficult Locates the items on the ability continuum

Item-free person ability Locates the person on the ability continuum

Places items and persons on the same scale – the ITEM MAP

IEA Teacher Education Study in Mathematics

3rd NRC Meeting, June 25-29, 2007. Taipei, Chinese Taipei.

Construct & Content Considerations

Statistics provide information that assists with decision making

Item selection or retention should be based on informed professional judgment

Does the item contribute in important ways to the content domain coverage