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Related Concept Videos

Transformations of Functions III01:20

Transformations of Functions III

Transformations modify the graphical representation of a function without changing its fundamental form. One common transformation is reflection, which flips the graph across a designated axis. When the vertical coordinates of all points are multiplied by the negative one, the entire graph is mirrored over the horizontal axis. This transformation reverses the vertical orientation of peaks and troughs, akin to signal inversion in electrical systems, where a waveform is flipped, but the timing of...
Transformations of Functions II01:29

Transformations of Functions II

Transformations in mathematics alter the position or orientation of a function’s graph while preserving its fundamental shape. One important type of transformation is the horizontal shift, which involves modifying the input variable within a function’s equation. This operation affects where outputs occur along the horizontal axis but does not alter the function’s overall structure.A horizontal shift is achieved by replacing the input variable x with either x + c or x - c, where c is a constant.
Exponents01:30

Exponents

Exponents provide a compact and efficient way of representing repeated multiplication. These tools are fundamental to algebra and broader areas of mathematics, including scientific computation, scaling laws, and dimensional analysis.Exponent Rules and PropertiesExponential notation expresses the repeated multiplication of a number by itself. For any nonzero real number a and integer n, an represent a multiplied by itself n times. Key properties include: These properties allow for the...
Transformations of Functions I01:29

Transformations of Functions I

A function's graph can be modified by changing its position or size without altering its overall shape. These transformations allow the graph to be moved across the coordinate plane while preserving its pattern and structure. One of the most common transformations is shifting, which repositions the graph without distorting it.When the output of a function is adjusted by adding or subtracting a constant, the graph shifts vertically. A positive value moves the graph upward, while a negative value...
Properties of DTFT I01:24

Properties of DTFT I

In signal processing, Discrete-Time Fourier Transforms (DTFTs) play a critical role in analyzing discrete-time signals in the frequency domain. Various properties of the DTFTs such as linearity, time-shifting, frequency-shifting, time reversal, conjugation, and time scaling help understand and manipulate these signals for different applications.
The linearity property of DTFTs is fundamental. If two discrete-time signals are multiplied by constants a and b respectively, and then combined to...
Convolution: Math, Graphics, and Discrete Signals01:24

Convolution: Math, Graphics, and Discrete Signals

In any LTI (Linear Time-Invariant) system, the convolution of two signals is denoted using a convolution operator, assuming all initial conditions are zero. The convolution integral can be divided into two parts: the zero-input or natural response and the zero-state or forced response, with t0 indicating the initial time.
To simplify the convolution integral, it is assumed that both the input signal and impulse response are zero for negative time values. The graphical convolution process...

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Related Experiment Video

Updated: Jun 24, 2026

RBDT: A Computerized Task System based in Transposition for the Continuous Analysis of Relational Behavior Dynamics in Humans
11:09

RBDT: A Computerized Task System based in Transposition for the Continuous Analysis of Relational Behavior Dynamics in Humans

Published on: July 17, 2021

Children's multiplicative transformations of discrete and continuous quantities.

Hilary Barth1, Andrew Baron, Elizabeth Spelke

  • 1Department of Psychology, Wesleyan University, Middletown, CT 06459, USA. hbarth@wesleyan.edu

Journal of Experimental Child Psychology
|March 18, 2009
PubMed
Summary
This summary is machine-generated.

Children

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Multimedia Battery for Assessment of Cognitive and Basic Skills in Mathematics (BM-PROMA)
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Multimedia Battery for Assessment of Cognitive and Basic Skills in Mathematics (BM-PROMA)

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Related Experiment Videos

Last Updated: Jun 24, 2026

RBDT: A Computerized Task System based in Transposition for the Continuous Analysis of Relational Behavior Dynamics in Humans
11:09

RBDT: A Computerized Task System based in Transposition for the Continuous Analysis of Relational Behavior Dynamics in Humans

Published on: July 17, 2021

Multimedia Battery for Assessment of Cognitive and Basic Skills in Mathematics (BM-PROMA)
10:58

Multimedia Battery for Assessment of Cognitive and Basic Skills in Mathematics (BM-PROMA)

Published on: August 28, 2021

Area of Science:

  • Cognitive Development
  • Numerical Cognition

Background:

  • An early-emerging analog magnitude system represents numerical quantity.
  • This system supports basic whole number computations in young children and nonhuman primates.

Purpose of the Study:

  • To investigate if the analog magnitude system supports predictions about halving and doubling transformations.
  • To explore the role of this system in the development of rational number concepts.

Main Methods:

  • 138 kindergartners and first graders reasoned about quantities after halving or doubling.
  • Stimuli included dot arrays and bars, with controls for non-numerical features.
  • Tasks assessed predictions of quantity changes.

Main Results:

  • Children's predictions indicated the use of halving and possibly doubling transformations on numerical quantities.
  • Evidence suggests these computations are applied to both discrete and continuous representations.
  • Performance was observed before formal instruction in multiplication or division.

Conclusions:

  • The analog magnitude system appears to support basic multiplicative transformations in young children.
  • This capability may be foundational for developing an understanding of rational numbers.
  • Early numerical cognition extends to non-symbolic multiplicative reasoning.