The teaching-learnig of Graph Theory with the

“The teaching-learning of Graph Theory with the support of Learn Graph-Ware software” José Alfredo Jiménez-Murillo, Eréndira Miriam Jiménez-Hernández, Octavio Ortíz-Ortíz, Juan Carlos Olivares-Rojas and Paola Jiménez-Hernández Ixtapa, México, November 8-10, 2017

Outline • Introduction • Graph Theory • Learn Graph-Ware • Statistical Analysis of the Results • Conclusions Ixtapa, México, November 8-10, 2017

Introduction

Ixtapa, México, November 8-10, 2017

Introduction

Ixtapa, México, November 8-10, 2017

Introduction

Ixtapa, México, November 8-10, 2017

Graph Theory

Ixtapa, México, November 8-10, 2017

Discrete Mathematics

Ixtapa, MĂŠxico, November 8-10, 2017

Graph Theory

Ixtapa, México, November 8-10, 2017

Graph Theory r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 a b c d e

1 0 0 0 0

0 1 0 1 0

1 1 0 0 0

1 0 0 0 1

0 0 1 0 0

0 1 1 0 0

1 0 1 0 0

0 1 0 1 0

0 0 1 1 0

0 0 0 1 1

Ixtapa, México, November 8-10, 2017

Graph Theory • Applications of graphs.

• The optimization of resources • Pattern recognition • Evaluation of mathematical expressions • Evaluation of lines of code in a programming language Ixtapa, México, November 8-10, 2017

Graph Theory

Ixtapa, México, November 8-10, 2017

Learn Graph-Ware

Ixtapa, México, November 8-10, 2017

Learn Grap-Ware

Ixtapa, México, November 8-10, 2017

Learn Grap-Ware

Ixtapa, México, November 8-10, 2017

Learn Graph-Ware

Ixtapa, México, November 8-10, 2017

Statistical Analysis of the Results • In order to do this, it was necessary to divide the 54 students studying Discrete Mathematics into two groups of 27. One of these groups was denominated as the experimental group, while the other was called the control group.

• The students were placed in the groups in a random fashion. The experiment took place in the August to December semester of 2016.

Ixtapa, México, November 8-10, 2017

Statistical Analysis of the Results • This was done by using the Student’s t-Test to measure the difference in the means obtained by both groups, with a confidence interval of at least 95%. The following hypotheses were established: • H0: The means of the final scores obtained by the two groups are the same.

• H1: The means of the final scores obtained by the two groups are significantly different.

Ixtapa, México, November 8-10, 2017

Statistical Analysis of the Results • These results and other statistical elements appropriate to the testing of the hypotheses were obtained using IBM SPSS Statics© software.

Group Experimental Control

N 27 27

Mean of Standard standard Mean deviation error 83.15 9.757 1.878 76.11

11.722

2.256

Ixtapa, México, November 8-10, 2017

Statistical Analysis of the Results Independent Samples Test Levene’s Test t-test for for Equality Equality of Means of Variances Equal variances assumed Equal variances not assumed

F

Sig.

t

gl

Sig. (2-tailed)

0.986

0.325

2.397

52

0.020

2.397

50.343

0.020

Ixtapa, MĂŠxico, November 8-10, 2017

Statistical Analysis of the Results Motivation Factors Parameter Mean Standard Deviation Attention Relevance Confidence Satisfaction

4.27 4.18 4.31 4.35

0.61 0.72 0.63 0.66

Ixtapa, MĂŠxico, November 8-10, 2017

Conclusions • The students in the experimental group had the experience of resolving more problems with the support of the LGW software, which allowed them to observe, analyze and understand the properties and paths in the graphs.

• The results obtained show that the students were highly motivated when using this software, while the average mean shows that their academic performance was considerably better than that of the students in the other group.

Ixtapa, México, November 8-10, 2017

Questions?

• José Alfredo Jiménez-Murillo ppalf@yahoo.com • Eréndira Miriam Jiménez-Hernández erendira.jimenez@ciencias.unam.mx • Octavio Ortíz-Ortíz octavioortiz@itmorelia.edu.mx • Juan Carlos Olivares-Rojas jcolivares@itmorelia.edu.mx • Paola Jiménez-Hernández paolaj@itmorelia.edu.mx Ixtapa, México, November 8-10, 2017