Related Experiment Video
Updated: Jun 1, 2026
10:58
Multimedia Battery for Assessment of Cognitive and Basic Skills in Mathematics (BM-PROMA)
Published on: August 28, 2021
Understanding and using principles of arithmetic: operations involving negative numbers
Richard W Prather1, Martha W Alibali
1Department of Psychology, University of Wisconsin-Madison.
Cognitive Science
|June 4, 2011
Summary
Adults understand arithmetic principles for negative numbers, linking this knowledge to how they represent math problems. Better understanding of negative number arithmetic leads to more accurate equation setup.
Area of Science:
- Cognitive Psychology
- Mathematics Education
Background:
- Prior research explored adults' understanding of arithmetic principles with positive numbers.
- This study investigates adults' knowledge of arithmetic principles involving negative numbers.
Purpose of the Study:
- To extend previous work by examining adults' knowledge of negative number arithmetic principles.
- To explore the relationship between knowledge of these principles and problem representation strategies.
Main Methods:
- Forty-four adult participants completed two tasks: an Evaluation task and a Word Problem task.
- In the Evaluation task, participants judged the correctness of equations, some violating arithmetic principles.
- In the Word Problem task, participants formulated equations for given word problems.
Main Results:
- Participants correctly identified and rated non-violation sets higher than violation sets for subtraction with negative numbers.
- Greater knowledge of negative number arithmetic principles correlated with a higher likelihood of using negative numbers in equation setup.
Conclusions:
- Adults demonstrate an understanding of core arithmetic principles when working with negative numbers.
- Knowledge of negative number arithmetic principles influences how individuals represent and solve mathematical problems.
Related Concept Videos
01:27Real Number Operations
The concept of real numbers includes all the values that can be represented on a continuous number line. The system began with basic counting values used for enumeration. It later expanded to include values that represent the absence of quantity and opposites of the counting values. When situations required expressing parts of a whole or dividing quantities evenly, values capable of representing such proportions were developed. When written using decimal notation, these values can end or repeat...
01:29Complex Numbers
The real number system cannot represent the square root of a negative number, which restricts solutions for certain equations, such as quadratics with negative discriminants. To address this, the complex number system was developed, introducing the imaginary unit i, where i = √(-1). This extension allows for the representation of all roots, including those involving negative radicands.A complex number is written in the form x + yi, where x and y are real numbers. Here, x represents the real...
01:28Rational Expressions
Rational expressions are algebraic fractions in which both the numerator and the denominator are polynomials. These expressions follow the arithmetic rules of numerical fractions but require extra care due to the presence of variables. A fundamental part of working with rational expressions is identifying values that make the expression undefined, typically those that result in division by zero or undefined radicals.Determining the DomainThe domain of a rational expression includes all real...
01:29Quadratic Equations in the Complex Number System
A quadratic equation in the form ax2+bx+c=0 can have solutions that vary in nature depending on the value of the discriminant, b2−4ac. In this expression, a is the coefficient of the quadratic term x2, b is the coefficient of the linear term x, and c is the constant term. When the discriminant is negative, the equation has no real number solutions. However, by introducing complex numbers through the imaginary unit i, defined by i=-1, these equations can still be solved.The square root of a...
01:28Inequalities
Inequalities express mathematical relationships where two values are not equal and are compared using symbols such as <, >, ≤, or ≥. These expressions define a range of possible solutions rather than a single value. Interval notation provides a concise way to express these solution sets, especially when the variable spans a continuous range. An open interval, written as (a, b), excludes the endpoints, while a closed interval [a, b] includes them. There are also half-open intervals, such...
01:26Algebraic Expressions
Algebraic expressions are essential in mathematics. They represent relationships through variables, constants, and operations. These expressions help describe patterns and solve problems in various mathematical fields. Understanding their components, classifications, and operations allows for efficient simplification and manipulation.Each algebraic expression consists of individual parts, including numbers and symbols, that work together to form meaningful mathematical statements. The numerical...