Alicia Bruno

The teaching of numerical extensions: the case of negative numbers

Some results of a study on the teaching of negative numbers are presented. Attention is concentrated on a unified view of the teaching of numbers. This ideais based on three dimensions of the numerical knowledge: abstract, contextual and number line. The research was carried out with 127–13-year-old students and is focused on the identification of addition and subtraction, the use of the number line, additive problem solving and the possibility of following several sequences of numerical extensions. Results show the importance of previous ideas on positive numbers and how these ideas influence the knowledge of negative numbers. Also included are the resolution procedures used by the students for additive problems. Interviews with 11 students allow analysis of their different levels of understanding of the objectives of the experience.

Learning subtraction and addition through digital boards: a Down syndrome case

AbstractThis paper examines key issues involving the interaction, design and usability of a digital whiteboard interface to support Down syndrome (DS) students in their learning of addition and subtraction algorithms. The research goals include (a) to identify the main interaction difficulties present when executing addition and subtraction operations and (b) to improve the interaction design of the digital whiteboard interface to adapt it to DS characteristics. In order to achieve these goals, several studies (usability and educational) were conducted with experts and children. These methods and techniques included prototyping, questionnaires (pre-post), thinking out loud, video-recording and structured observation. As regards the interaction aspects with the whiteboard, the items evaluated included (a) mouse use, (b) placement of numbers and balls, (c) ball deletion and crossing out, (d) placement of the sign of the operation and (e) use of sensitive areas established in the worksheet. In addition, the paper presents the main strategies, procedures and errors of DS students for carrying out addition and subtraction algorithms that are more predominant in the DS population. Some relevant findings and results are presented, such as the importance of visual aids (graphics, balls, fingers, etc.) in teaching addition and subtraction to individuals with DS, the advantages of using the whiteboard for students who have difficulty writing, as they can focus on the operation at hand and forget their difficulties with handwriting, or mathematical errors arising from interaction issues.

Verification and validation of an intelligent tutorial system

This paper presents the results of a verification and validation process for an intelligent system. The system being studied is an Intelligent Tutorial that employs fuzzy logic and multiagent systems. Software engineering techniques were used in the verification process, while the validation exploited both qualitative and quantitative techniques.

Fuzzy and MultiAgent Instructional Planner for an Intelligent Tutorial System

This article presents some aspects in our research into the design of a Fuzzy and MultiAgent Instructional Planner belonging to an Intelligent Tutoring System (ITS), which has been designed as a tool for the reinforcement of the addition operation. The authors propose the combined use of both fuzzy and MultiAgent Systems. The fuzzy logic methodology is used to model the students knowledge and the teaching strategy. Furthermore, the MultiAgent System implemented determines the learning objectives so as to provide the student with an efficient learning process. The fuzzy and MultiAgent Systems comprising the instructional planner were verified with the collaboration of experts in mathematics and in other areas of knowledge. The results obtained by the primary school children who used the ITS are also presented.

Strategies of Pre-Service Primary School Teachers for Solving Addition Problems with Negative Numbers.

This paper analyses the strategies used by pre-service primary school teachers for solving simple addition problems involving negative numbers. The findings reveal six different strategies that depend on the difficulty of the problem and, in particular, on the unknown quantity. We note that students use negative numbers in those problems they find easy and resort to other strategies in more complex problems. Furthermore, the problem-solving strategies reveal lingering difficulties involving negative numbers, such as mistakes with arithmetic rules and a lack of rigour in the mathematical notation used in the operations.

Addition and subtraction by students with Down syndrome

We present a research report on addition and subtraction conducted with Down syndrome students between the ages of 12 and 31. We interviewed a group of students with Down syndrome who executed algorithms and solved problems using specific materials and paper and pencil. The results show that students with Down syndrome progress through the same procedural levels as those without disabilities though they have difficulties in reaching the most abstract level (numerical facts). The use of fingers or concrete representations (balls) appears as a fundamental process among these students. As for errors, these vary widely depending on the students, and can be attributed mostly to an incomplete knowledge of the decimal number system.

Teacher strategies simulation by using fuzzy systems

Fuzzy system technologies are of emerging interest in the specification and implementation of complex systems. This article introduces fuzzy instructional planner, which models the tutor module in a intelligent tutorial system (ITS). The behaviour of this system is defined by strategies which adapt the learning process for individual students by applying appropriate pedagogical methodologies. For this reason, the purpose of a instructional planner is to mimic the behaviour of the teacher able to control learning process satisfactorily. The knowledge acquisition is based on the reasoning carried out by the teacher in a learning process. Usually, this information is obtained from human expert who supplied linguistic information. The capacity to use linguistic information is specific to fuzzy inference systems.

Inclusive educational software design with agile approach

In this paper we present a proposal of inclusive educational software design based on principles of user-centered design (UCD), user experience design (UXD) and agile methodologies (SCRUM). The main goal of this proposal is to identify usability problems and UX factors in early stages of educational software development for users with special educational needs. Furthermore, we also present a User Interface (UI) design and its evaluation conducted with experts and students. This UI evaluation has been divided in several phases, using diverse methods with different actors. Prototyping and usability heuristics are presented as a fast and cost-efficient but still effective and accurate evaluation method for user experience with educational software.