# Enriching Elementary School Mathematical Learning with the Steepest Descent Algorithm

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

## 3. Results

^{2}. With three movements, the probability decreases to (1/8)

^{3}. The probability of randomly getting all three questions right in 3 moves each is (1/8)

^{3}(1/8)

^{3}(1/8)

^{3}= 0.000000008. This means that choosing neighboring cells at random gives an expected score of 0.0000008 points. The real expected score is even lower since some trajectories are longer than 3 moves. Thus, in practical terms, the probability of answering correctly by chance is zero. Similarly, for Item 2 the expected score is 0.19 points when choosing at random. For Item 3, selection by chance gives 50 points. This means that the teachers and students in our study scored above chance with a 95% confidence level. The closest to chance is Item 3. However, the scores minus the Confidence Interval (CI) width do not hit the chance score. Therefore, the score is above chance with a 95% confidence level. Interestingly, the students performed significantly better than the teachers on Item 3 (Figure 7). This is indeed the only item where students did better than teachers. However, we have to consider a critical fact: that only 76.7% of the students answered this item, compared with 98.9% of the teachers. Item 4 has 5 options. Therefore, the expected score is 20 points when choosing at random.

## 4. Discussion

## 5. Conclusions

## Supplementary Materials

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Screenshot of Item 1. Note that this item has three questions. The user has to mark the path that the bacteria will follow, which always move to the neighboring cell with the highest number (the number represents the amount of nutrients), until they no longer find a higher number.

**Figure 3.**Screenshot of Item 2. Here, the user has to connect the blue cell and then consecutively connect the cells through which the dog passes, considering that it always moves to the neighboring cell with the highest number (the number represents the intensity of the smell), until it no longer finds a neighboring cell with the highest number (i.e., where the bone is).

**Figure 5.**Screenshot of Item 3. In this item, the user has to consider the same rule of motion as in Item 2 and then connect the board that represents a courtyard where two bones are hidden in different places.

**Figure 6.**Screenshot of Item 4. Here the user has to consider the same rules of motion as in Items 2 and 3 and then connect the cell in blue whose number should be changed in order for the dog to always find the bone located at the yellow cell no matter where it starts.

Subjects | N | % Item 1 | % Item 2 | % Item 3 | % Item 4 |
---|---|---|---|---|---|

Teachers | 457 | 99.6 | 99.3 | 98.9 | 98.9 |

Students | 90 | 42.2 | 95.6 | 76.7 | 72.2 |

Subjects | Item 1 | Item 2 | Item 3 | Item 4 |
---|---|---|---|---|

Teachers | 52.3 | 59.7 | 60.8 | 56.8 |

Students | 43.2 | 49.7 | 77.5 | 50.1 |

Chance | 0 | 0.19 | 50 | 20 |

Subjects | Item 1 | Item 2 | Item 3 | Item 4 |
---|---|---|---|---|

Teachers | 730 | 537 | 204 | 140 |

Students | 478 | 219 | 78 | 79 |

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**MDPI and ACS Style**

Araya, R. Enriching Elementary School Mathematical Learning with the Steepest Descent Algorithm. *Mathematics* **2021**, *9*, 1197.
https://doi.org/10.3390/math9111197

**AMA Style**

Araya R. Enriching Elementary School Mathematical Learning with the Steepest Descent Algorithm. *Mathematics*. 2021; 9(11):1197.
https://doi.org/10.3390/math9111197

**Chicago/Turabian Style**

Araya, Roberto. 2021. "Enriching Elementary School Mathematical Learning with the Steepest Descent Algorithm" *Mathematics* 9, no. 11: 1197.
https://doi.org/10.3390/math9111197