Related Experiment Video
Updated: Dec 21, 2025

11:29
Measuring the Functional Abilities of Children Aged 3-6 Years Old with Observational Methods and Computer Tools
Published on: June 20, 2020
9.6K
Learning the Concept of Function With Dynamic Visualizations
Tobias Rolfes1, Jürgen Roth2, Wolfgang Schnotz3
1IPN - Leibniz Institute for Science and Mathematics Education, Kiel, Germany.
Frontiers in Psychology
|May 20, 2020
Summary
Dynamic visualizations significantly improve learning of the concept of function for secondary students compared to static representations. Interactivity within visualizations did not further enhance learning outcomes.
Area of Science:
- Mathematics Education
- Cognitive Science
Background:
- Understanding the concept of function is crucial in mathematics.
- Traditional static representations may pose challenges for student comprehension.
- Dynamic visualizations offer potential for improved learning experiences.
Purpose of the Study:
- To compare the effectiveness of static representations versus dynamic visualizations for learning the concept of function.
- To investigate the impact of interactivity within dynamic visualizations on learning outcomes.
- To explore potential aptitude-treatment interactions with visual-spatial ability.
Main Methods:
- A laboratory experiment involving 157 secondary-school students.
- Comparison of learning outcomes between static representations and two types of dynamic visualizations (linear and interactive).
- Assessment of visual-spatial ability to identify aptitude-treatment interactions.
Main Results:
- Students demonstrated significantly better learning with dynamic visualizations compared to static representations.
- No significant difference in learning outcomes was found between linear and interactive dynamic visualizations.
- No significant aptitude-treatment interaction was observed between visual-spatial ability and the learning methods.
Conclusions:
- Dynamic visualizations are more effective than static representations for teaching the concept of function.
- The level of interactivity in dynamic visualizations does not appear to significantly affect learning outcomes.
- Visual-spatial ability does not moderate the effectiveness of dynamic versus static representations in this context.
Related Concept Videos
Introduction to Functions
142
Functions are essential mathematical tools used to describe consistent relationships between varying quantities. A function connects each input to a single, corresponding output based on a defined rule. These relationships appear in both everyday contexts and natural phenomena, providing a framework for understanding change and prediction.One common real-life example is a parking garage fee system, where the total cost depends on the amount of time a vehicle remains inside. In this case, the...
142
Graphs of Functions
142
Graphs of functions provide a visual representation of how output values change in response to varying inputs. Each point on the graph corresponds to an ordered pair, where the x-coordinate (independent variable) determines the horizontal position and the y-coordinate (dependent variable) determines the vertical position. Linear functions like y = x give a straight line, indicating a constant rate of change.Nonlinear functions display more complex behaviors. Even power functions generate...
142
Introduction to One-to-one Functions
102
A one-to-one function is a mathematical function in which each element of the domain maps to a distinct and unique element in the range. This property ensures that no two different inputs result in the same output, formally expressed as f (x1) ≠ f (x2) whenever x1 ≠ x2. The graphical criterion for identifying such functions is the Horizontal Line Test, which indicates that a function is one-to-one if and only if no horizontal line intersects its graph at more than one point.A...
102
Types of Functions I
161
Functions are fundamental mathematical tools that capture relationships between variables and describe how one quantity changes in relation to another. Their diverse forms allow them to model various real-world phenomena with precision and flexibility. Among the various categories, algebraic functions are prominent due to their formulation through basic arithmetic operations: addition, subtraction, multiplication, division, and root extraction.Algebraic functions include polynomial, rational,...
161
Types of Functions II
103
Trigonometric and exponential functions are essential mathematical tools used to model distinct types of real-world behavior, particularly in periodic and growth-related phenomena. These functions extend the capabilities of basic algebraic models by capturing recurring cycles and rapid changes across various scientific and engineering contexts.Trigonometric functions, such as sine and cosine, are particularly effective for representing periodic phenomena. Their cyclic behavior makes them...
103
Transformations of Functions III
98
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...
98

