M. Gloria Sánchez-Torrubia M. Asunción Sastre-Rosa Víctor Giménez-Martínez

1. APPLIED MATHEMATICS DEPARTMENT UNIVERSIDAD POLITÉCNICA DE MADRID SPAIN PEDAGOGICAL IMPACT OF INTERACTIVE TUTORIALS IN VISUALIZATION AND LEARNING OF MATHEMATICAL CONCEPTS IN COMPUTER SCIENCE CURRICULA M. Gloria Sánchez-Torrubia M. Asunción Sastre-Rosa Víctor Giménez-Martínez Carmen Escribano-Iglesias Applied Mathematics Department Universidad Politécnica de Madrid

2. OVERVIEW • Visualization in teaching and learning maths. • Requirements in a pedagogical visualization tool. • Impact of interactive tools on maths learning. • Aiding the teacher. • Aiding the student. • Providing final term projects. • Interactive Tutorials in our web site: • Differentiation. • Fleury’s algorithm. • Conclusions and further work. • Overview • Visualization in teaching and learning maths • Requirements in a pedagogical visualization tool • Impact on maths learning • Teacher • Student • Final Term P • Tutorials in our web site • Differentiation • Fleury’s • Conclusions and further work

3. VISUALIZATION IN TEACHING AND LEARNING MATHS • Overview • Visualization in teaching and learning maths • Requirements in a pedagogical visualization tool • Impact on maths learning • Teacher • Student • Final Term P • Tutorials in our web site • Differentiation • Fleury’s • Conclusions and further work • Visualization enhances comprehension, engagement and satisfaction among students. • A group of teachers’ observations*: • 90% teaching experience more enjoyable; • 86% improved student participation; • 83% class more exciting for students; • 76% basis for discussing conceptual foundations; • 52% objective evidence of improved student learning. • *Naps et al. Exploring the role of Visualization and Engagement in CSE

4. REQUIREMENTS IN A PEDAGOGICAL VISUALIZATION TOOL • Overview • Visualization in teaching and learning maths • Requirements in a pedagogical visualization tool • Impact on maths learning • Teacher • Student • Final Term P • Tutorials in our web site • Differentiation • Fleury’s • Conclusions and further work • Ease of use. • Insightful and visual. • Interactivity (providing inputs or predicting next step). • Platform independence. • No installation or maintenance tasks. • Clear concepts’ explanations in hypertext format.

5. IMPACT OF INTERACTIVE TOOLS ON MATHS LEARNING • Overview • Visualization in teaching and learning maths • Requirements in a pedagogical visualization tool • Impact on maths learning • Teacher • Student • Final Term P • Tutorials in our web site • Differentiation • Fleury’s • Conclusions and further work • Graphs and graph algorithms play an important role in computer science engineering education. • Graphs are structures that need to be visualized. • Other mathematical concepts also need a visual dynamical tool. • Visualization provides a basis for understanding conceptual foundations. • Interactivity shows a huge potential for achieving didactical goals.

6. AIDING THE TEACHER • Overview • Visualization in teaching and learning maths • Requirements in a pedagogical visualization tool • Impact on maths learning • Teacher • Student • Final Term P • Tutorials in our web site • Differentiation • Fleury’s • Conclusions and further work • Some mathematical concepts include dynamic structures difficult to show in static tools. • Lectures become easier and more efficient. • If the application waits for the next entry, it provides time to explain the current step. • Students’ attention and participation are enhanced.

7. AIDING THE STUDENT • Overview • Visualization in teaching and learning maths • Requirements in a pedagogical visualization tool • Impact on maths learning • Teacher • Student • Final Term P • Tutorials in our web site • Differentiation • Fleury’s • Conclusions and further work • Insight is substantially improved. • Interest and engagement are increased. • Learners spend more time when visualization is involved. • Students who have to interact with the applet, learn much more than those who passively look at visualizations. • Leads to higher learning results.

8. PROVIDING FINAL TERM PROJECTS • Overview • Visualization in teaching and learning maths • Requirements in a pedagogical visualization tool • Impact on maths learning • Teacher • Student • Final Term P • Tutorials in our web site • Differentiation • Fleury’s • Conclusions and further work • Last year students: • Develop the tools under teachers’ design and supervision. • Review maths concepts. • Feel proud of helping younger colleagues. • Maths teachers: • Do not have to seek and learn didactical software. • The tool fits exactly their needs.

9. JAVA TUTORIALS IN OUR WEB SITE • http://www.dma.fi.upm.es/java/ • Tutorials’ features: • Contain theoretical explanations of related maths concepts. • Are easy to use, visual and interactive. • Need no installation or maintenance. • Have demonstrated to help us improving learning results. • Overview • Visualization in teaching and learning maths • Requirements in a pedagogical visualization tool • Impact on maths learning • Teacher • Student • Final Term P • Tutorials in our web site • Differentiation • Fleury’s • Conclusions and further work

10. Differentiation • Overview • Visualization in teaching and learning maths • Requirements in a pedagogical visualization tool • Impact on maths learning • Teacher • Student • Final Term P • Tutorials in our web site • Differentiation • Fleury’s • Conclusions and further work www.dma.fi.upm.es/java

11. Fleury’s algorithm • Overview • Visualization in teaching and learning maths • Requirements in a pedagogical visualization tool • Impact on maths learning • Teacher • Student • Final Term P • Tutorials in our web site • Differentiation • Fleury’s • Conclusions and further work www.dma.fi.upm.es/java

12. CONCLUSIONS AND FURTHER WORK • Overview • Visualization in teaching and learning maths • Requirements in a pedagogical visualization tool • Impact on maths learning • Teacher • Student • Final Term P • Tutorials in our web site • Differentiation • Fleury’s • Conclusions and further work • For the students enhance: • comprehension; • memorization; • satisfaction. • When the teacher makes use of them increases: • interest; • motivation. • Java interactive tutorials are very good aids for maths learning

13. CONCLUSIONS AND FURTHER WORK • Overview • Visualization in teaching and learning maths • Requirements in a pedagogical visualization tool • Impact on maths learning • Teacher • Student • Final Term P • Tutorials in our web site • Differentiation • Fleury’s • Conclusions and further work • Creating libraries containing exercises. • Saving the user’s work. • By Java Web Start. • By signed applets. • Implementing new algorithms: • Karnaugh maps and QuineMcCluskey’s algorithm; • differentiation on two variables; • Gauss method for solving liner equation systems.

14. THANKS • Overview • Visualization in teaching and learning maths • Requirements in a pedagogical visualization tool • Impact on maths learning • Teacher • Student • Final Term P • Tutorials in our web site • Differentiation • Fleury’s • Conclusions and further work M. Gloria Sánchez-Torrubia M. Asunción Sastre-Rosa Applied Mathematics Department Universidad Politécnica de Madrid