Virtual Reality vs Real Virtuality in Mathematics Teaching And Learning

The paper presents research activities carried out within DALEST Project (Developing an Active Learning Environment for the Learning of Stereometry). Some of the computer 3D applications based on Elica are considered together with possible educational activities in the context of nets of solids. The first impressions of the pilot experiment are presented from learners’, educators’; and developer’s perspective

Mathematical Modelling Using Technology in Elementary School

The purpose of the present study was twofold; first to examine students’ mathematization processes as they worked on a mathematical modelling problem and second to investigate students’ interactions with Potters Wheel, which is a computer software for generating solids by revolution. One group of three students worked for two 40 minute sessions on “Soft Drink Bottle” modelling activity. The activity required students to construct models for a soft drink bottle. The results of the study provide evidence that Potters Wheel assisted students in developing the necessary mathematical constructs and processes to actively engage and solve the problem through meaningful mathematical modelling. Students’ mathematical development included creating models for defining appropriate bottles, finding and relating variant and invariant measures such as volume and surface. Finally, implications for further research are discussed

Words Are Silver, Mouse Clicks Are Gold?

How do we teach children to express and communicate ideas in a formal and informal mode? What type of language do they need in a concrete context? How should they determine a proper level of formalization of their descriptions? In an attempt to explore these issues we carried out an experiment with 5th graders from three Bulgarian schools during which the students experienced the whole process of generating a good description – becoming aware of the ambiguity, producing counterexamples, reducing the ambiguity, eliminating the redundancy. The educational scenarios and the Cubix Editor (an Elica-Logo application) used in the experimental activities were developed in the frames of the DALEST European project. The first impressions confirm our belief that the language is playing significant role in the learning experiences of the students, that the relationship between thoughts and words involves back and forth reshaping process. While constructing and describing cubical structures they articulated their own ideas, developed concepts collaboratively with others, moved between everyday and mathematical terms, between procedural and declarative style, exploring the boundaries of understanding. Such interplay with the step-wise refinement of their descriptions of cubical structures would hopefully enhance students’ skills for working with mathematical definitions, on one hand, and prepare them for writing, debugging and explaining programs, on the other

Developing an Active Learning Environment for the Learning of Stereometry

This paper reports on the design of a dynamic environment for the learning of stereometry (DALEST) and the teaching of spatial geometry and visual thinking. The development of the software was in the framework of DALEST project which aimed at developing a dynamic threedimensional geometry microworld that enables students to construct, observe and manipulate geometrical figures in space, and to focus on modelling geometric situations. The environment will also, support teachers in helping their students to construct a suitable understanding of stereometry. During the developmental process of software applications the key elements of spatial ability and visualization were carefully taken into consideration with emphasis on enhancing dynamic visualization as an act of construction of transformations between external media and student’s mind

(De-)Coding adventures for young researchers

We often associate coding with writing secret messages; however, this is usually called encrypting. Coding is a more general notion meaning to represent a message using specially designed symbols (AKA codes). Codes are not only the symbols used to code a message (sorry for this recursive statement), but are also the rules that control the processes of using these codes. The sole goal of a code is to be decoded. When we talk about secret codes, the goal becomes to make decoding easy for specific recipient and impossible to everybody else. This represents the encryption meaning of coding. In Greek kryptos means hidden. The other word that is often used for coding secret messages, is ciphering. The origin of this word leads us to the Arabic word sifr, meaning zero, empty, nothing. It has been introduced in Europe by the arrival of the Arabic numerals and soon its meaning has become not just zero, but also any numeral. Later on, it has started to be used for coded messages. Nowadays the cipher is usually a code based on digits

Human Impact Factor in the Research and Development of Educational Software

This paper presents the long-term impact factor which a single person may have on a researcher. This is a description of the author’s research topics and the creation of educational software, which were either directly or indirectly affected by Prof. Edward Friedman. ACM Computing Classification System (1998): A.0, D.2.6, I.3.4, I.6.8, J.2, J.6, K.3.1

Enhancing Spatial Imagination of Young Students by Activities in 3D Elica Applications

The paper presents research activities carried out within DALEST Developing an Active Learning Environment for the Learning of Stereometry).Some of the computer 3D applications based on Elica are considered together with possible educational scenarios

Design and Implementation of a Logo-based Computer Graphics Course

Two years ago the Faculty of Mathematics and Informatics at Sofia University makes a decision to design a new series of Logo-based courses which make use of the modern technology. The pedagogical component of the challenge is to design a multidisciplinary course suitable for students with different skills and interests. From a development perspective the challenge is to build an entirely new one. And finally the course must be attractive regardless of the seriousness and complexity of the topics included in it. The paper discusses the structure of the course including the final weeks when topics emerging from students’ course projects are taught. Each lesson from the course is based on sets of sample programs representing the general lifecycle of software development. This includes designing, coding and debugging. Samples are created on-the-fly, thus different instances of the course results in different final projects. Lessons are interactive and students may interfere with the direction of demonstrated software development. Three lessons from the course are sketched in the paper. The first one is taught in week 4 and spans over Computer Science, Calculus, Analytical Geometry; and Applied Statistics and Probability. The lesson in week 6 is focused on composition of complex movements and their synchronization. It uses elements from Computer Science, Geometry, Physics, and Trigonometrics. The third lesson is about relative transformational geometry and its application in the form of Turtle Graphic

Re-experiencing Engineering Inventions within a Modern Virtual Environmen

This paper describes a personal journey in the world of Mathematics and Mechanics and the actual process of reinventing devices with focus on their mathematical and mechanical properties. A set of important accompanying skills have been identified along the path of constructing these devices

Wild Programming – One Unintended Experiment with Inquiry Based Learning

This paper describes one unplanned experiment of a 6th grade student writing her first computer program for 3D graphics before learning any programming language. Some intriguing aspects in her program are analyzed, especially the emerging understanding of key concepts like enumeration, naming conventions of variables and symmetry in 3D space. The paper also identifies two main directions of mental processes. The first direction is actively supported by the school. It is based on presenting and using knowledge in a distilled error-free way. The other direction encompasses techniques needed to identify wrong solutions and to find a way to overcome problems and reach a correct solution. This direction in underrepresented in the educational system and as a result, it is left uncultivated. Students are expected to develop such skills by themselves