Teaching Derivatives Concepts with Computational ...

Teaching Derivatives Concepts with Computational Techniques.

J.M. Silva, A.C. Carius, M. M. Pereira and D.F. Jardim

University of the Valleys of Jequitinhonha and Mucuri UFVJM ICME-13, Hamburg, 2016

Outline

1

Introduction

2

The classroom activities

3

Discussions

4

References

Introduction Outline

1

Introduction

2

The classroom activities

3

Discussions

4

References

Introduction Introduction

This work presents a qualitative analysis about teaching Calculus I with computational techniques using software in a classroom at the interdisciplinary Science and Technology Bachelor Course from the Federal University of Jequitinhonha and Mucuri Valleys. This analysis presents a continuation of the studies about the work that we are developing in UFVJM teaching Calculus and Physics with computational modeling techniques. In this work our main purpose is to discuss and evaluate the challenge of teaching and learning derivatives concepts using GeoGebra in a freshmen students class.

Introduction UFVJM

The mission is to produce and spread knowledge and innovation by integrating teaching, research and extension services as propellers of regional and national development. The institution stands out for its importance to the economic and sociocultural development of the region by generating employment and income as well as reducing social inequality.

Mucuri Campus at Teolo Otoni-MG since 2006.

Introduction UFVJM

There are more than 130 projects exclusively in charge at UFVJM, and nine other national projects in which it takes part.

Science and Technology. Institute for Science, Technology and Engineering.

Introduction UFVJM

In this context it is a great challenge to teach Mathematics in the Interdisciplinary Science and Technology Bachelor course with students with so many social and structural problems.

Water Engineering. Construction Engineering.

Introduction Introduction

We believe that the technology can provide a better understanding of some mathematical concepts and ideas that are still abstract to the students. As (D'Ambrosio, 2015) said, the transfer of knowledge, particularly of technology, is a crucial issue in the analysis of the process of development. Then we use this tool to create visual information about the concepts discussed and presented by the teacher.

Introduction Introduction

The students that arrive as freshman in the STB have a great lack of mathematical and physical concepts coming from the High School. It is very important that these students can to describe and understand a natural phenomenon that needs mathematical representation. (D'Ambrosio, 2009) said, the learning process should not be just to stimulate the reproduction of concepts, neither repetition nor memorization. Then, to search an appropriate methodology for the teaching of mathematics is essential.

Introduction The Didactic Engineering

Researchers who follow the didactics of mathematics line search to adapt teaching methodologies through a sequential structure for the learning process. They focus on work in the classroom and challenging activities as a stimulus in the production and construction of the mathematical knowledge. The Didactic Engineering (Artigue, 1996) for example, proposed by researchers in France, follows this thinking and the four steps: A priori analysis Experimentation A posteriori analysis Validation

Introduction The Didactic Engineering

The work proposed here is part of a step sequence presented at the Didactic Engineering and uses technology to encourage and propose challenges to students in the classroom, enhancing the work of the students and the teaching activity. By analyzing the characteristics of mathematical teaching and learning cases, two viewpoints have been presented on teaching this course in this work: The instructor teach (i.e., the teaching goal) The learned by the students (i.e., the orientation of the learning).

The classroom activities Outline

1

Introduction

2

The classroom activities

3

Discussions

4

References

The classroom activities The classroom activities The classroom activities were divided in two classes: STB-A with 59 students STB-B with 58 students

The classroom activities The classroom activities

After a few hours of teaching training using theoretical concepts and exploring denitions, theorems and dierentiability techniques by the teacher, a research group called Group of Studies in Free Software (GESE) proposed a small workshop using GeoGebra. In this course were explored the derivatives concepts that the teacher has taught in the classroom. Along this small workshop GESE also helped the students to nish and understand some exercises proposed by the teacher.

The classroom activities Modeling-Missile Launch

Teaching the concepts of tangent, maximum and minimum in problem that involves the movement of a pendulum.

The classroom activities Pendulum Movement

Teaching the concepts of tangent, maximum and minimum in problem that involves the movement of a pendulum.

The classroom activities Modeling

The classroom activities Modeling

Discussions Outline

1

Introduction

2

The classroom activities

3

Discussions

4

References

Discussions Discussions

It is important to point here that with this teaching technology methodology the students are able to develop the ability to nd the responses by themselves using denitions and theorems and also by the use of technology using GeoGebra software. In this sense, these approaches complement each other. As a teacher strategy and a goal to promote a co-operative environmental only between students, the GESE group worked with the students without the presence of the teacher.

Discussions Discussions

In the future, we will insert the teacher in a negotiation environment and evaluate his presence in the students thinking, considering his inuence as a negotiator of knowledge that can leads the students to their conclusions. This is an important conclusion because these students in particular, prefer to work with the presence of the teacher also in the workshop because they feel more secure about their mathematical thinking conclusions

References Outline

1

Introduction

2

The classroom activities

3

Discussions

4

References

References References Araujo, J. L., Campos, I. S. (2015). Negotiating the Use of Mathematics in a Mathematical Modeling Project. In: Stillman, G. and Blum, W. and Bibemgut, M. S. and (Eds). Mathematical Modeling in Education Research and Practice. Cap.23, p. 283-292. New York: Springer. Artigue, M. (1990) Ingénierie didactique. Recherches en Didactique des Mathématiques, vol. 9, n◦ 3, pp. 281307. La Pensée Sauvage. Artigue, M. and Perrin - Glorian, M.(1991) Didactic Engineering, Research and Development Tool: Some Theoretical Problems Linked to This Duality. Vol. 11, No. 1, pp. 13-18.

References References Kaiser, G. and Sriraman, B. (2006). A global survey of international perspectives on modelling in mathematics education. ZDM The International Journal on Mathematics Education, 38(3), 302-310. Morrison, F. (1991). The Art of Modeling Dynamics Systems. Forecasting for Chaos, Randomness, and Determinism. Nova Jersey: John Wiley and Sons. Palharini, B. and Almeida, L. M. W. (2015). Mathematical Modeling Tasks and the Mathematical Thinking of Students. In: Stillman, G. and Blum, W. and Bibemgut, M. S. and (Eds). Mathematical Modeling in Education Research and Practice. Cap.17, p. 219-228. New York: Springer.