DEVELOPING MATHEMATICAL ABILITIES USING LEARNING OBJECTS WHEN LEARNING NUMERICAL METHODS
Numerical methods for solving initial value problems are included in syllabus of Engineering careers, because many problems that arise in different fields of Engineering are modelled by differential equations with initial conditions, initial value problems (IVP), and their solutions are too difficult to obtain, or even do not exist.
When teaching issues of Mathematics, it is important to analize the mathematical abilities achieved by students, and contrast that with what faculty pretended. There are different ways to do this and professors should select the appropriate tools.
In order to do this in numerical analysis courses at Facultad Regional San Nicolás (FRSN), Universidad Tecnológica Nacional (UTN) from Argentina, some activities were designed using apps developed with Mathematica, where students can select and apply methods to solve problems, and analize the validity of the solution obtained. These apps are CDF (Computable Document Format) files, which need Mathematica for their development of them, but when running them only the CDF Player is needed, which is available in the Web without restrictions.
In particular, when teaching numerical methods for solving IVP, some activities were proposed using a CDF file designed especially with the purpose to analize the mathematical abilities achieved by students when learning this issue. This file is an app where the input needed to run is the differential equation, and the initial conditions and the number of nodes conforming the discretization of the domain. Once data has been loaded, a method must be selected to obtain the approximate solution and the final global error.
The mathematical abilities analized with this didactic resource are given by the revised Bloom´s Taxonomy. This classification distinguishes six levels that the student must overcome in order to produce a true learning process.
These levels are:
• Remember: retrieves, recalls or recognizes knowledge from memory.
• Understand: constructs meanings from different types of functions, whether in written or graphical way.
• Apply: performs or uses a procedure during the development of a representation or implementation.
• Analyze: decomposes into material or conceptual parts and determines how they are related to or interrelated with each other, or with a complete structure, or for a particular purpose
• Evaluate: makes judgments based on criteria and standards using verification and critique.
• Create: joins elements together to form a coherent and functional whole, reorganizing elements into a new pattern or structure by generating, planning or producing.
This work aims to show the designed CDF and some activities proposed to the students along with the rubric that was used to analyze each one of the answers given by them. The results obtained and some reflections about the learning achieved by the students are also presented.