Related Experiment Video
Updated: May 16, 2026
10:58
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
Journal of Applied Measurement
|December 14, 2012
Summary
This study validated cognitive attributes for an eighth-grade math test, finding 17 attributes reliable. Performance on these attributes was similar between genders but lower in eastern regions for students.
Area of Science:
- Educational Measurement
- Cognitive Psychology
- Mathematics Education
Background:
- Cognitive attributes are crucial for understanding student performance in mathematics.
- Validating these attributes is essential for accurate assessment and targeted interventions.
- Previous research has not fully established a comprehensive set of cognitive attributes for eighth-grade mathematics.
Purpose of the Study:
- To validate a comprehensive set of cognitive attributes for an eighth-grade mathematics test.
- To compare student performance across these validated attributes based on gender and region.
- To identify and refine predictive cognitive attributes using empirical data.
Main Methods:
- Utilized the least squares distance method for attribute validation.
- Analyzed data from 5,000 eighth-grade students from the 2005 Turkish national mathematics assessment.
- Assessed 25 mathematics items for the presence or absence of 20 initial cognitive attributes.
Main Results:
- Four of the initial 20 cognitive attributes were identified as misspecified or nonpredictive.
- The study validated a revised set of 17 cognitive attributes.
- No significant performance differences were found between male and female students on the attributes.
- Students from two eastern regions demonstrated significantly lower performance on most attributes compared to other regions.
Conclusions:
- The revised set of 17 cognitive attributes provides a valid framework for assessing eighth-grade mathematics.
- Gender is not a significant factor in performance on these cognitive attributes.
- Regional disparities in educational resources or opportunities may contribute to underperformance in specific geographic areas.
Related Concept Videos
01:11Residuals and Least-Squares Property
The vertical distance between the actual value of y and the estimated value of y. In other words, it measures the vertical distance between the actual data point and the predicted point on the line
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...
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...
01:20Calibration Curves: Linear Least Squares
A calibration curve is a plot of the instrument's response against a series of known concentrations of a substance. This curve is used to set the instrument response levels, using the substance and its concentrations as standards. Alternatively, or additionally, an equation is fitted to the calibration curve plot and subsequently used to calculate the unknown concentrations of other samples reliably.
For data that follow a straight line, the standard method for fitting is the linear...
For data that follow a straight line, the standard method for fitting is the linear...
01:20The Distance Formula
In geometry, measuring the direct distance between two points on a plane is essential in various practical and theoretical applications. Whether in navigation, engineering, or computer graphics, determining the shortest path between two locations involves using the distance formula. This formula is derived from the Pythagorean Theorem, which relates the lengths of the sides of a right triangle. On a coordinate plane, the horizontal and vertical distances between two points serve as the legs of...
01:25Systems of Linear Equations in Two Variables
Solving a system of linear equations is a fundamental concept in algebra. A system of equations consists of two or more linear equations involving the same set of variables. One of the most efficient algebraic methods for solving such systems is the substitution method. This technique involves expressing one variable in terms of the other from one equation and substituting it into the second equation. This method is particularly useful when one of the equations is easily rearranged.Consider the...
01:20Midpoint Rule
Approximating areas under curved boundaries is a common problem in applied mathematics, particularly when an exact calculation is difficult or impractical. One effective numerical method for this purpose is the Midpoint Rule, which provides an estimate of the area under a curve by using rectangular approximations over a specified interval.Description of the Midpoint RuleThe Midpoint Rule begins by dividing the given interval into a number of equal subintervals. For each subinterval, the...
01:24Area Computation by the Alternative Coordinate Method
The alternative coordinate method, also known as the Shoelace Formula, is a technique for determining the area of a traverse using Cartesian coordinates. This method relies on the sequential arrangement of x and y coordinates for each point of the shape, ensuring accuracy and ease of application.In this approach, each corner's x and y coordinates are listed as fractions, with the x-coordinate as the numerator and the y-coordinate as the denominator. These coordinates are arranged sequentially...