Spatial ability – the capacity to mentally visualize, rotate, and manipulate objects – is one of several skills that predict achievement in STEM (Science, Technology, Engineering, and Mathematics). People with strong spatial skills can imagine how a structure fits together, picture a molecule in 3D, or mentally navigate complex environments. These abilities are especially important in fields such as physics and engineering, where visualizing spatial relationships is central to problem-solving.
However, not all STEM fields rely on spatial thinking in the same way. Fields like biology or computer science tend to depend less on it. Even so, people who perform well on spatial tasks are more likely to pursue and succeed in STEM careers.
Measuring spatial skills
Cognitive psychologists measure spatial ability through a range of well-validated tasks, each designed to tap a specific component of spatial reasoning, such as spatial visualization, spatial orientation, and spatial perception.
One of the classic tasks is the mental rotation task (pictured below), originally developed by Shepard and Metzler in 1971 (cited over 9,000 times, according to Google Scholar). In this task, participants view two complex 3D shapes made of connected blocks, as shown in the figure below. The shapes are rotated to different angles, and participants must quickly and accurately decide whether they are the same object (just rotated) or mirror images of each other.
The mental rotation task is considered a measure of rigid spatial skills, in which the shapes maintain their structure as they’re rotated. These rigid transformations are central to tasks like imagining how a mechanical part fits into a machine or how geometric shapes relate to one another in space.
But what about objects that don’t stay the same shape?
Non-rigid (ductile) spatial thinking
In the real world, many spatial problems involve non-rigid or ductile spatial reasoning – thinking about objects that bend, fold, stretch, or twist. Examples include folding fabric, sculpting clay, or visualizing how protein chains fold in molecular biology.
The paper folding task, for example, asks participants to imagine folding a sheet of paper several times and then punching a hole through it. They must then choose the correct pattern of holes that would appear when the paper is unfolded. This is an example of a non-rigid spatial task because the paper changes shape through folding.
Until recently, researchers had few tools to measure these flexible, real-world kinds of spatial reasoning, which limits our understanding of how non-rigid spatial skills develop and contribute to STEM learning.
The Knot Reasoning Task
To address this gap, Grace Bennett‑Pierre, Thomas Shipley, Nora Newcombe, and Elizabeth Gunderson (pictured below) developed a new measure of non-rigid, ductile spatial skill: the knot reasoning task.
As the name suggests, the task requires participants to reason about knots, a perfect example of flexible spatial structure. The team designed three types of items, shown in the figure below:
- Backwards reasoning items: participants see a target picture of a knot-tying step and four possible images showing earlier steps. Their task is to identify which image shows the step that came immediately before the target. See panel A in the figure below.
- Different materials items: The target knot is made from one material (e.g., heavy rope), while the options were made of a different material (e.g., yarn). See panel B in the figure below.
- Pulling items: participants view a knot and decide whether it would come apart if one end were pulled. See panel C in the figure below.
What they found
In Study 1, 279 participants (134 women, 135 men, 8 non-binary) completed the knot reasoning task. The overall reliability was excellent (α = 0.88), and participants averaged 71% correct. Breaking down performance by subscales resulted in the backwards reasoning items being hardest, the different materials items being intermediate, and the pulling items being easiest.
Interestingly, women outperformed men on the different material items, suggesting possible advantages in tasks requiring attention to surface features or material properties.
In Study 2, 147 participants (82 women, 56 men, 9 nonbinary/other) completed the knot reasoning task alongside several established spatial measures, including the mental rotation task, paper folding task, bending task, and a vocabulary task. They also completed the Spatial Activities Questionnaire, which assesses engagement in activities that foster spatial skills (like puzzles, model building, drawing, or crafts).
The knot reasoning task correlated positively with all other spatial measures, including both rigid and non-rigid ones, supporting its validity. However, the results did not support a simple continuum between rigid and non-rigid skills, which implies that these two types of spatial reasoning may rely on partially distinct cognitive processes.
When comparing performance by gender, men outperformed women on most spatial measures (mental rotation, paper folding, and vocabulary), but not on the bending task.
The role of spatial activities
The researchers also explored how engagement in different types of spatial activities might explain gender differences. Surprisingly, the results didn’t follow the expected pattern.
Men who reported greater engagement in masculine-stereotyped spatial abilities (such as video gaming, building, or sports involving spatial coordination) actually performed worse on the mental rotation and knot reasoning tasks. In contrast, women who engaged in more feminine-stereotyped spatial activities (such as crafts or arts) performed better on the paper-folding task.
For the knot reasoning task specifically, engaging in feminine-stereotyped spatial activities was linked to higher scores on backwards reasoning items, suggesting that fine-grained, detail-oriented spatial experiences might enhance certain non-rigid skills.
Finally, although students in math-intensive STEM majors (such as physics or engineering) had slightly higher average spatial scores, the differences among math-intensive, non-math-intensive STEM, and non-STEM participants were not statistically significant.
Why it matters
Bennett‑Pierre and colleagues’ work fills a gap in spatial cognition research. Most existing measures, like mental rotation, assess how people manipulate rigid shapes. The new knot reasoning task opens the door to studying a more flexible, real-world form of spatial reasoning that better captures how we think about materials, motion, and change.
This research also broadens our understanding of how gender and experience shape spatial thinking. While traditional rigid tasks often show an advantage for men, the pattern for non-rigid tasks may differ, and even reverse under certain conditions. That finding has implications for how we teach and foster spatial reasoning across disciplines.
As the authors conclude,
“The studies in this paper offer a new method for testing under-studied non-rigid, ductile spatial skills. In addition to advancing theoretical research on the structure of spatial skills, the current studies will also allow future work to investigate whether non-rigid spatial skills uniquely contribute to STEM and arts learning.”
By expanding how we measure spatial ability, researchers are helping to build a more complete picture of the cognitive tools that support problem-solving: from rotating objects to tying knots in our minds.
Featured Psychonomic Society paper
Grace Bennett-Pierre, Thomas F. Shipley, Nora S. Newcombe, & Elizabeth A. Gunderson (2025). Developing a novel measure of non-rigid, ductile spatial skill. Cognitive Research: Principles & Implications, 10, 13. https://doi.org/10.1186/s41235-025-00621-w
