CASual learning of mathematical concepts
What is it about?
- GeoGebra, TI-Nspire and ClassPad are so innovative technological tools that even their developers seem to be unaware of their huge potential for the learning of new concepts! Among millions of pages on the Internet, there are only examples how a tool or application can be used for this or that operation. In those cases, the user should not only know a lot of the concepts beyond those operations but also quite a lot about the commands of that particular tool or application.
- The starting point of this book is totally opposite: The user does not need to know almost anything about the conceptual knowledge to be studied or the commands of the tool or application.
What are the ideas based on?
- The approach is based on dynamic linking of different representation forms, especially between algebra and dynamic geometry.
- Knowledge appears for the user ("learner") on two levels: Spontaneous procedural knowledge and more or less abstract conceptual knowledge. Learning means building bridge between these knowledge types by manipulating whichever of those two.
- Theories of Piaget and Vygotsky are not applied by "going just on one-way street" : Experience -> Concept -> Symbol but taking the position that technology allows to activate abstract and concrete knowledge simultaneously.
Does this theory have research-based evidence?
- Yes, largely. Professor Lenni Haapasalo has introduced his long-term research
in several publications and conferences. He has based his teacher-education on this approach for more than 15 years, which means that there are several clinical studies also made by his student teachers. One of those talent students is the second author Olli Karkkulainen who has adopted this theory when acting as service-in-trainer for CAS technology, especially TI-nspire calculator.
- Last but not at least, it is appropriate to mention the own "Piaget Laboratory" of Professor Haapasalo: his children (born -93,-94, -95 and -97). Their everyday actions have offered more relevant practical theory of knowing and learning than literature - assumed the observer has enough basic theories to allow make relevant interpretations of how children think and what all they are able to construct.
Why the book is appearing so late as now?
- Very good question. The most important reason is that now technological applications have reached the level where the above-mentioned theory of knowing and learning can be applied in the way Professor Haapasalo has wanted. This regards especially the so-called Simultaneous Activation principle. Another reason is that by introducing three different products at the same time, the book is free from any advertisement contamination and can therefore be offered for official institutions. This has been emphasized by the metaphor of rock-paper-scissors: None of those three applications is overwhelming because everyone of those tools can offer its own comfort zone for the user depending of the topic.
How can I study the basic philosophy beyond the book?
Is there some kind of e-support available?
- For those who buy the book, there will be interactive applets on the Internet.
- More information about a possible forum as "donate area" will be given later on.
For whom is the book aimed, actually?
- As a matter of fact for anybody who would like to play with mathematics. Perhaps the right place would be a supermarket because the threshold to begin to make own mathematics is low.
- It does not make any sense to write the book only for the teachers because even a small child can construct most of the concepts in the book. A typical example is the gradient of a straight line through origin, which was invented in about 15 minutes by a 5 years old son of a teacher student of Professor Haapasalo.
- The GeoGebra pictures, for example, have been made at the very beginning in more than 20 languages, waiting to be implemented in multilingual versions of the book.
What is going to be the price of the book?
- As a matter you can influence on that by making a pre-order, which effects on the edition volume.
- At this very stage the estimated price is between 30 € and 40 € but books can bee printed locally in any country according to which kind of contract will be made with MEDUSA.
Can I get support for using and applying the book?
- Of course. If you are an innovative user, professor Haapasalo has a great pleasure to act as a supervisor even for a doctoral thesis.
Do I want to take a look on the content?