Malleability of Spatial Reasoning With Short-Term and Long-Term Robotics Interventions

Abstract

Spatial reasoning correlates with academic success in mathematics and science, is highly malleable, and can be learned. Yet, spatial reasoning is often underused, underdeveloped, and ignored in current grade-school curriculum and teaching. This study explores changes in elementary students’ spatial reasoning skills after participation in either a short-term or a long-term robotics intervention. The robotics intervention and the spatial elements within the intervention tasks are described. Measures of spatial reasoning elements were administered before and after each intervention. Two different groups of students ages 9–10 years were tested: a short-term group (N = 11) and a long-term group (N = 48). Statistical analysis revealed significant improvements to several different elements of spatial reasoning in both groups. Findings suggest that programming robots in either the short- or long-term intervention was associated with improvements in spatial reasoning.

Appendix A

1.1 Measures and Spatial Skills Assessed

1.1.1 Sorby Drawing Items

These test items were based on Sorby’s (2012) idea of combining solid objects. For these tests, students had to identify which parts of a 2D representation of a 3D shape were inside or outside of the combined object. They then had to trace the lines corresponding to either the inside or outside of the combined objects.

All test items were assessed on a 5-point scale. The following exemplary evaluation criteria indicates the scoring for Sorby drawing items: Perfect (5/5), nearly perfect (4/5), correct portion of box or cylinder (not both) or somewhat incomplete (3/5), very incomplete but on the right track (2/5), outlined whole object, whole box, parts of whole object or nothing (0/5). Below is an example of an unmarked item on the left and a marked 4/5 item on the right

Fig. 7

Sorby drawing test item. Score 4/5

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Spatial Reasoning in Sorby Drawing Items. In terms of spatial reasoning skills, the task required SENSATING and SITUATING since students had to imagine and visualize the intersecting 3D object as shown in the 2D diagram. Thereby, they also engaged in dimension shifting and intersecting. Envisioning the inside and the outside object required additional spatial reasoning skills of the [DE]CONSTRUCTING category, since the construction of the intersecting object was realized by decomposing the outside or intersecting (interior) edges of the combined object, as well as by determining how the objects fit together (fitting). Students then had to trace the edges corresponding to the inside and the outside of the object, which is described in the INTERPRETING group of spatial skills (i.e., diagramming).

1.1.2 Paper Folding Items

For these questions, an image of a piece of paper was folded and then had holes punched in it or had a corner cut out. The students had to identify what the paper would look like once unfolded. They were given multiple options to choose from and had to circle one. Partial marks were awarded if the student chose a reflection along the y-axis (e.g., lower left corner)

Fig. 8

Paper folding test item. Score 5/5

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Spatial Reasoning in Paper Folding Items. Students were required to imagine the reflection of the hole punches or cut corner in the unfolded paper and visualize the corresponding solution to the task (both skills are elements of the SENSATING category). They were given multiple options to choose from and were required to circle one. Spatially, the task also required skills from the ALTERING, INTERPRETING, and MOVING categories since students had to imagine the folded paper (folding), the symmetrical pattern formed from the fold (symmetrizing), as well as the reflections created by hole punches or the cut corner in the unfolded paper (reflecting). Simultaneously, locating, orienting, and decomposing skills were required to determine the holes and cut corners in the unfolded paper (these are elements of the SITUATING and [DE]CONSTRUCTING group of spatial skills).

1.1.3 Shape Rotation Items

For these questions, students were asked to identify shapes that could be found by rotating the exemplified 2D shape (i.e., the shape could not be reflected).

Fig. 9

Shape rotation Item. Score 5/5

Spatial Reasoning in Shape Rotation Items. Since the task required finding the rotated 2D shape in correct orientations, rotating and orientating spatial reasoning skills from the MOVING and SITUATING categories were needed. As students imagined and visualized the shape’s rotation, they drew on elements of the SENSATING category. Finally, the task also required comparing and relating the original position of the shape to rotations and reflections of the same shape, both of which are spatial reasoning skills of the INTERPRETING subset.

1.1.4 Stereonet (2D to 3D Cube) Item

Students were asked to visualize folding a cube out of a 2D stereonet. The first item required finding the correct tabs or drawing missing tabs to hold all the edges of the cube together. The second item required recognizing a triangular pattern on the 3D cube shown in the 2D stereonet (not shown in Fig. 10. 

Fig. 10

Stereonet (2D to 3D Cube) test item. Score 4/5

The item shown below scored a 4/5. It is missing one tab.

Spatial Reasoning in Stereonet (2D to 3D Cube) Item. The task required visualizing and imagining the resulting 3D shape found by folding the stereonet (SENSATING category). A multitude of additional spatial reasoning skills was required to imagine the resulting 3D shape, including ALTERING (folding), SITUATING (dimension shifting), INTERPRETING (comparing and relating 2D nets with the 3D shape), and [DE]CONSTRUCTING (composing the 3D shape). The first test item required finding the correct tabs or drawing missing tabs to hold all the edges of the cube together. The second item required recognizing the triangular pattern on a 3D cube as shown in the 2D stereonets. Spatially, these tasks rely on orienting skills when finding the corresponding tabs or corresponding triangular pattern on the resulting 3D cube (SITUATING category), as well as elements from the INTERPRETING subset when diagramming the tabs that hold the cube together.

1.1.5 Building a 3D Object From a Picture Item

Students were shown a picture of a 3D object made out of blocks. Then, the picture was taken away and they were asked to build the object from memory. 

Fig. 11

Building a 3D object from a picture test Item. Score 2/5

Spatial Reasoning in Building a 3D Object From a Picture Item. A variety of spatial reasoning skills was required for this task. Constructing a 3D object from a 2D image involves dimension shifting and several other spatial reasoning skills of the SITUATING and [DE]CONSTRUCTING categories. To build the object, students had to know where the blocks were in space and their orientation, as shown in the image. Locating and orienting skills were needed to identify where the blocks were positioned, and aspects of intersecting elements of the shape needed to be considered. Building also required composing, packing, arranging, sectioning and fitting blocks together (all elements of the [DE]CONSTRUCTING group of spatial reasoning skills). Moreover, the physical act of assembling the model required tactilizing and propriocepting spatial skills, both of which are part of the SENSATING class. Since the image is not to scale, visualizing and imagining skills support envisioning the composed object (SENSATING category). Finally, elements of the INTERPRETING class were also recognizable, since the construction of the 3D model (modelling) relied on comparing and relating the object to the initial image shown.

1.1.6 Moving a Shape on a Grid Item

Without the use of their fingers or pens, students were asked to visualize that a shape on a grid was moved 5 spaces to the right, 5 spaces up, and 8 spaces to the left. They were then asked to circle the intersection at which the shape ended up. In the scored item below, the student located the point one space too far left for a score of 4/5.

Fig. 12

Moving a shape on a grid item. Score 4/5

Spatial Reasoning in Moving a Shape on a Grid Item. When students were imagining and visualizing the movement of a shape on a grid, they were drawing on spatial reasoning skills from the SENSATING category. Spatially, imagining the shape move right, left, and up also required MOVING skills, i.e., sliding and directioning. Students were then asked to circle the intersection at which the shape ends up. It can be asserted that elements of the SITUATING subset were also required to solve this task, since the shape’s path had to be imagined (pathfinding), and the location at the end of the path had to found (locating).

1.1.7 Cross-section of a Cube: Isometric Projection Item

Students were asked to identify what 2D shape was produced by taking the diagonal cross-section of a cube from a selection of 2D shapes. Another way to approach the question was to identify what the shadow of the 2D shape would be if it were balancing on one corner (isometric projection)

Fig. 13

Cross-section of a cube test item. Score 0/5

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Spatial Reasoning in Cross-Section of a Cube Item. Imagining the cross section of the cube between two vertices required SENSATING (perspective-taking, visualizing, imagining). Selecting the cross-section of a 3D object on 2D paper required SITUATING (dimension shifting, orienting, intersecting), as well as INTERPRETING (modelling, comparing, relating).

1.1.8 Block Visualization/Rotation Item

Students were asked to match images of four 3D shapes to a corresponding reordered set of rotated images of the four 3D shapes.

Fig. 14

Block visualization/rotation item. Score 5/5

Spatial Reasoning in Block Visualization/Rotation Item. Students are asked to match images of four 3D shapes to a corresponding reordered set of rotated images of the four 3D shapes. In terms of spatial reasoning skills, this task required rotating and reflecting skills (MOVING category), while imagining and visualizing the rotated and/or reflected image of a 3D shape (SENSATING category). Images could be matched by comparing and relating the rotated and reflected shapes to the original four 3D images (INTERPRETING category) while using orienting and locating skills to identify the correctly matched image (SITUATING category).

1.1.9 Pattern Arranging Item

Students were asked to look at an arrangement of pattern block shapes on a 3 × 3 grid for 30 s. The shapes were then covered up and students were asked to arrange pattern blocks according to what they saw.

Fig. 15

Pattern arranging test item

Spatial Reasoning in Pattern Arranging Item. Several spatial reasoning skills were needed for this task, including SITUATING skills (i.e., locating the correct position of the pattern blocks and orienting them correctly), SENSATING skills (i.e., visualizing, imagining, and tactilizing the correct position and orientation of pattern blocks), MOVING skills (rotating the pattern blocks in the correct orientation), and [DE]CONSTRUCTING skills (i.e., arranging the pattern blocks on the grid).