Related Experiment Video
Updated: May 16, 2026

Multimedia Battery for Assessment of Cognitive and Basic Skills in Mathematics (BM-PROMA)
Published on: August 28, 2021
Cognitive assessment in mathematics with the least squares distance method
Lin Ma1, Emre Çetin, Kathy E Green
1Morgridge College of Education, University of Denver, Denver, CO 80208, USA. lma3@du.edu
Abstract:
This study investigated the validation of comprehensive cognitive attributes of an eighth-grade mathematics test using the least squares distance method and compared performance on attributes by gender and region. A sample of 5,000 students was randomly selected from the data of the 2005 Turkish national mathematics assessment of eighth-grade students. Twenty-five math items were assessed for presence or absence of 20 cognitive attributes (content, cognitive processes, and skill). Four attributes were found to be misspecified or nonpredictive. However, results demonstrated the validity of cognitive attributes in terms of the revised set of 17 attributes. The girls had similar performance on the attributes as the boys. The students from the two eastern regions significantly underperformed on the most attributes.
Related Concept Videos
Residuals and Least-Squares Property
If the observed data point lies above the line, the residual is positive, and the line underestimates the actual data value for y. If the observed data point lies below the line, the residual is negative, and the line overestimates the actual data value for y.
The process of fitting the best-fit...
Calibration Curves: Linear Least Squares
For data that follow a straight line, the standard method for fitting is the linear...
The Distance Formula
Systems of Linear Equations in Two Variables
Midpoint Rule
Area Computation by the Alternative Coordinate Method

