# Solving Problems through Engineering Design: An Exploratory Study with Pre-Service Teachers

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## Abstract

**:**

## 1. Introduction

## 2. Theoretical Framework

#### 2.1. The Teaching and Learning of Mathematics: Current Trends

#### 2.2. Perspectives about STEAM Integration

#### 2.3. Engineering Design in STEAM Education

#### 2.4. Summarizing

## 3. Method and Procedures

#### 3.1. Context and Participants

#### 3.2. The Moments in the Didactical Experience

#### 3.2.1. Moment 1—Preliminary Activities

#### 3.2.2. Moment 2—Implementation

#### 3.2.3. Moment 3—Dissemination

#### 3.2.4. Moment 4—Evaluation

#### 3.3. Data Collection and Analysis

## 4. Results from the Implementation of the Paper Table Problem

#### 4.1. The Participants along the Engineering Design Cycle

#### 4.1.1. Part 1. Exploring and Designing the Problem

#### 4.1.2. Part 2. (Re)Building, (Re)Testing and (Re)Designing

#### 4.1.3. Group Results

#### 4.2. Participants’ Engagement in the Didactical Experience

#### 4.2.1. Cognitive Engagement

#### 4.2.2. Affective Engagement

#### 4.2.3. Behavioral Engagement

## 5. Conclusions

## 6. Limitations

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 2.**Engineering Design Cycle (adapted from Cunningham and Hester [46]).

Levels of Engagement | Descriptors |
---|---|

Cognitive | Surface strategy (memorization; procedural knowledge; handling tests) Deep strategy (understanding; establish connections; justification) Reliance (pose questions; follow the teacher’s instructions) |

Affective | Interest (joy; pleasure; sense of satisfaction; curiosity; excitement) Achievement orientation (effort to get good results; focus on finishing a task) Anxiety (nervous, worried; afraid of poor results) Frustration (uncomfortable; tired; dislike for the task) |

Behavioral | Attentiveness (listen; take an active part in the discussion; make an effort; concentration) Diligence (effort to understand; try again; persistence) Time spent (on out-of-class learning) |

Engineering Design Process | Problem Solving Process (Adapted from Polya [59]) | |
---|---|---|

The problem | Understand the problem | Did I understand the problem? What is asked? |

Imagine (Brainstorm) | What do I need to know about the problem? Do I have enough information to solve the problem? | |

Design (Plan) | Devise a plan | Collect all the available information. Do I know a related problem? Did I use all the conditions? Can I use know strategies, like look for a pattern; draw a Figure? |

(re)Build (Create) | Carry out the plan | Carry out the previous plan. Select a strategy to solve the problem. Solve the problem |

(re)Test & Evaluate | Look back | Examine the solution. Does the answer/solution make sense? Does the solution fit the conditions? Does it work? |

Redesign (Improve) | Does the solution work? If not redesign it. Check each step. Can I find a simpler or better solution? | |

Share the Solution | Share the solution. |

Design Process | Description |
---|---|

Identify the Problem | Can I build a table that supports a book, without breaking down? |

Imagine | What kind of tables can I build? |

Design (plan) | Choose one table type. Draw a sketch of the table. |

(re)Build (create) | Did you follow the plan to create a model/prototype? |

(re)Test & Evaluate | Did the table support the book? |

Redesign (Improve) | Modify the table if it doesn’t fit the conditions or improve the model. Did you confirm the strength of the table legs? Did you build a table prototype? |

Share Solutions | Communicate your product. Create a poster where you summarize the used process and the STEAM contents. |

Engineering | Science | Mathematics | Art | Technology |
---|---|---|---|---|

Engage in the ED process. Identify and compare different basic types of tables (e.g., one, three, four legs), table support legs (e.g., triangular, cross, cylindrical) and discuss how these structures enhance stability and strength. Create, develop and communicate design ideas and processes. Build and share at least one paper table prototype that is able to hold a book for a minute. | Develop an understanding of the center of mass. Identify forces acting on different table types, including tension and compression. Understand how different table types support a book. Understand the resistance of the available materials. | Apply measurement skills and geometry concepts: polygons; solids; symmetries; … Identify the properties of polygons or solids correctly; … Apply spatial reasoning in working 2-D and 3-D shapes. Draw sketches using 2-D and 3-D representations. Use mathematical language correctly. Use problem solving strategies. | Show flexibility and divergent thinking. Show originality in design. Construct the artifact with aesthetic sense and perfection. | Look for types of tables in webpages. Consult webpages about tables’ resistance. |

Solids (38%) | Isolated/Simple Legs (46%) | Combined (16%) |
---|---|---|

Cubes | I-legs | Prism + legs |

Triangular prisms | V-legs | Cilinder + square Indian tent |

Square pyramids | X-legs | |

Cylinder | Legs in triangle Indian tent | |

Mixed solids | Legs in square Indian tent |

Disciplinary Area | Contents and Actions for Building Paper Table |
---|---|

Science | Develop basic understandings of centers of mass and forces Contribute to justify the balance and resistance of the table and the materials used Contribute to understand how different tables support a load |

Technology | Used spontaneously in the Imagine step, during brainstorming to discover types of tables |

Engineering | Contribute to recognize basic table types (e.g., one foot; four feet) and table structures (e.g., triangulation of the table legs) Engage participants in its design model to address and solve the problem (arrive at a consensus, test and retest) Recognize how the structures constructed enhance stability and strength |

Art | Contribute to creativity with the aesthetics features of the prototype of the table created (design, structure, design, overall look) Contribute to creativity with the aesthetics features in the elaboration and organization of the poster (e.g., disposition of the cycle and the sketches of the table, use of colors) |

Mathematics | Contribute to solve an authentic hands-on problem, using problem solving strategies (e.g., guess and check; logical reasoning, simulation) Construct arguments in group’s design and criticize their peers’ designs Understand the effect of using some concepts (e.g., shapes; pyramids; prisms, cubes; symmetry; estimation and measurements; perpendicularity; angles; weight) Spatial reasoning in recognizing, drawing and working with different 2-D and 3-D shapes and their representations |

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**MDPI and ACS Style**

Vale, I.; Barbosa, A.; Peixoto, A.; Fernandes, F. Solving Problems through Engineering Design: An Exploratory Study with Pre-Service Teachers. *Educ. Sci.* **2022**, *12*, 889.
https://doi.org/10.3390/educsci12120889

**AMA Style**

Vale I, Barbosa A, Peixoto A, Fernandes F. Solving Problems through Engineering Design: An Exploratory Study with Pre-Service Teachers. *Education Sciences*. 2022; 12(12):889.
https://doi.org/10.3390/educsci12120889

**Chicago/Turabian Style**

Vale, Isabel, Ana Barbosa, Ana Peixoto, and Fátima Fernandes. 2022. "Solving Problems through Engineering Design: An Exploratory Study with Pre-Service Teachers" *Education Sciences* 12, no. 12: 889.
https://doi.org/10.3390/educsci12120889