# Using Tangram as a Manipulative Tool for Transition between 2D and 3D Perception in Geometry

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## Abstract

**:**

## 1. Introduction

#### 1.1. Students’ Difficulties in Acquiring Spatial Skills

#### 1.2. Theoretical Framework

#### 1.3. Research Questions

## 2. Materials and Methods

#### 2.1. Tangram

#### 2.2. Action Research

#### 2.2.1. The Action Research Cycle

- (1)
- Reconnaissance or observation
- (2)
- Planning
- (3)
- Acting or monitoring
- (4)
- Reflecting or evaluating

#### 2.3. Participants

#### Characteristics of the Participants

#### 2.4. Measures

#### 2.4.1. Pre-Test

#### 2.4.2. The Tangram Tasks

- Draw a house, e.g., a square with a triangle on it. Divide the figure into two or more pieces (like puzzle pieces) and give them to a schoolmate to figure out what shape was cut out. The puzzle pieces can be put together individually and then exchanged between the children.
- Measure the sizes of a sample Tangram and then try to copy it on a sheet of paper.
- Discuss, what are the important data to look out for, when constructing on the paper.
- Make a Tangram out of cardboard, put it in an envelope, it will serve the class. Not all parts have to be used what enables free creation. Use items also from multiple sets at once. Make photographs of the results.
- Lay out new pictures, draw them around, and add lines to divide them into pieces.

## 3. Results

#### 3.1. Results of the Pre-Test

#### 3.2. Evaluation of the Tangram Tasks

## 4. Discussion

- Spatial perception such as: orientation in space, experiencing space, understanding spatial relationships.
- Spatial representation (mostly in 2D) such as: representing mutual positions in space or mutual positions in a mental visual image, representation of motion in space through time, reconstruction of space elements.
- Creation of spatial objects in 2D or 3D such as: modelling and construction.

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

## References

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**Figure 3.**Four phases of action inquiry cycle according to [18].

**Figure 12.**Example of ‘Making new figures’ from [25].

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**MDPI and ACS Style**

Kmetová, M.; Nagyová Lehocká, Z. Using Tangram as a Manipulative Tool for Transition between 2D and 3D Perception in Geometry. *Mathematics* **2021**, *9*, 2185.
https://doi.org/10.3390/math9182185

**AMA Style**

Kmetová M, Nagyová Lehocká Z. Using Tangram as a Manipulative Tool for Transition between 2D and 3D Perception in Geometry. *Mathematics*. 2021; 9(18):2185.
https://doi.org/10.3390/math9182185

**Chicago/Turabian Style**

Kmetová, Mária, and Zuzana Nagyová Lehocká. 2021. "Using Tangram as a Manipulative Tool for Transition between 2D and 3D Perception in Geometry" *Mathematics* 9, no. 18: 2185.
https://doi.org/10.3390/math9182185