Download Intelligent Learning Environments: The Case of Geometry by Eugène Chouraqui, Carlo Inghilterra (auth.), Jean-Marie PDF
By Eugène Chouraqui, Carlo Inghilterra (auth.), Jean-Marie Laborde (eds.)
This booklet is a completely revised consequence, up to date to mid-1995, of the NATO complicated examine Workshop on "Intelligent studying Environments: the case of geometry", held in Grenoble, France, November 13-16, 1989. the most target of the workshop was once to foster exchanges between researchers who have been eager about the layout of clever studying environments for geometry. the matter of pupil modelling used to be selected as a primary topic of the workshop, insofar as geometry can't be diminished to procedural wisdom and as the importance of its complexity makes it of curiosity for clever tutoring process (ITS) improvement. The workshop focused round the following issues: modelling the information area, modelling pupil wisdom, layout ing "didactic interaction", and learner regulate. This publication includes revised models of the papers awarded on the workshop. the entire chapters that stick to were written by means of members on the workshop. each one shaped the root for a scheduled presentation and dialogue. Many are suggestive of analysis instructions that may be performed sooner or later. There are 4 major matters operating in the course of the papers awarded during this e-book: • wisdom approximately geometry isn't really wisdom concerning the genuine international, and materialization of geometrical items implies a reification of geometry that is amplified in terms of its implementation in a working laptop or computer, considering gadgets will be manipulated at once and family members are the result of activities (Laborde, Schumann). This element is definitely exemplified by means of examine tasks targeting the layout of geometric microworlds (Guin, Laborde).
Read or Download Intelligent Learning Environments: The Case of Geometry PDF
Best geometry books
Conceptual Spaces: The Geometry of Thought
Inside of cognitive technological know-how, methods at present dominate the matter of modeling representations. The symbolic method perspectives cognition as computation regarding symbolic manipulation. Connectionism, a different case of associationism, versions institutions utilizing man made neuron networks. Peter Gardenfors bargains his conception of conceptual representations as a bridge among the symbolic and connectionist techniques.
There's an primarily “tinker-toy” version of a trivial package deal over the classical Teichmüller area of a punctured floor, referred to as the embellished Teichmüller house, the place the fiber over some extent is the distance of all tuples of horocycles, one approximately every one puncture. This version ends up in an extension of the classical mapping category teams known as the Ptolemy groupoids and to definite matrix types fixing similar enumerative difficulties, every one of which has proved helpful either in arithmetic and in theoretical physics.
The Lin-Ni's problem for mean convex domains
The authors turn out a few sophisticated asymptotic estimates for optimistic blow-up strategies to $\Delta u+\epsilon u=n(n-2)u^{\frac{n+2}{n-2}}$ on $\Omega$, $\partial_\nu u=0$ on $\partial\Omega$, $\Omega$ being a gentle bounded area of $\mathbb{R}^n$, $n\geq 3$. specifically, they convey that focus can ensue basically on boundary issues with nonpositive suggest curvature while $n=3$ or $n\geq 7$.
- Harmonic Analysis and Boundary Value Problems
- Leonardo da Vinci’s Giant Crossbow
- Problems in Plane Geometry (Science for Everyone)
- Algebraic geometry and its applications
- Lectures on Discrete and Polyhedral Geometry
- Student Solutions Manual for Linear Algebra with Applications
Extra info for Intelligent Learning Environments: The Case of Geometry
Example text
This feature is useful in order to find what remains invariant and what changes as one passes from a special case to a more general one. 42 T. Dreyfus and B. Schwarz Most typical activities with stereometrix are of the type: Predict and check. The learning experience is then based on the conflict arising if the prediction was incorrect. e. of cognitive information. In such a case, the translation of cognitive activity into microworld operations is irreversible. There are two types of exceptions to this.
2 Generalization A total of 63 students' performance on a pair of subtraction problems, like 4 - 2 and 2 - 4 (after being tested on commutativity of addition), was examined (The results of the individual children's answers are listed in Appendix I). Their responses to the second of the pair of problems fell in one of the following categories: i) "cannot be done" or "not possible", ii) "zero", iii) applied commutativity - copied the answer to the previous problem, iv) subtracted the smaller number from the larger one.
Another possible reason for generalization is that the children do not have a concept of negative numbers, which is the prerequisite knowledge for solving problems like 4 - 7 so they attempt a repair. One of these repairs happens to be applying commutativity. The children who give '0' or "nothing" as answers do not all have the same reason for their answers. ", some of them revealed that there is nothing left to subtract from after subtracting 2 (of the 4) from 2; some explained that there is nothing left Modelling Children's Informal Arithmetic Strategies 25 after subtracting 2 (of the 4) from 2 and hence the answer is O.