Mindstorms: Children, Computers, and Powerful Ideas

This powerful image of child as epistemologist caught Papert's imagination while he was working with Piaget. Piaget’s great insight was that knowledge is not delivered from teacher to learner;ather, children are constantly constructing knowledge through their everyday interactions with people and objects around them. If we really look at the “child as builder,” we are on our way to an answer. All builders need materials to build with. Where Papert's at variance with Piaget is in the role he attribute to the surrounding cultures as a source of these materials. Most saliently the models and metaphors suggested by the surrounding culture.

In today's digital age, children are using computers with increasing frequency. This is not only a requirement for school but also a crucial component of learning at home. Through computers, children gain access to a wealth of educational resources, thereby stimulating their imagination and creativity. For instance, children can use code to design simple games, which not only teaches them mathematics and logical thinking but also fosters a spirit of teamwork.

In this book, Papert not only introduces the application of computers in mathematics education but also deeply explores the importance of the learning process itself. He posits that learning should be active exploration rather than passive reception. Only through this approach can children truly fall in love with mathematics and flexibly apply it in their future lives.

Papert's discussion of the QWERTY keyboard metaphor makes us realize that many fixed patterns within educational systems can actually be challenged. Educators should try to break these frameworks and expose students to more diverse learning methods. For example, by integrating mathematics and art and understanding mathematical principles through design and creation, this type of interdisciplinary learning not only enhances students' interest but also cultivates their comprehensive literacy.

Seymour Papert：「I see “school math” as a social construction, a kind of qwerty. A set of historical accidents (which shall be discussed in a moment) determined the choice of certain mathematical topics as the mathematical baggage that citizens should carry. In order to break this vicious circle Papert want to lead the reader into a new area of mathematics, Turtle geometry, that he and his colleagues have created as a better, more meaningful first area of formal mathematics for children.

• Continuity principle: The mathematics must be continuous with well-established personal knowledge from which it can inherit a sense of warmth and value as well as “cognitive” competence.
• Power principle: It must empower the learner to perform personally meaningful projects that could not be done without it.
• Cultural resonance principle: The topic must make sense in terms of a larger social context. I have spoken of Turtle geometry making sense to children. But it will not truly make sense to children unless it is accepted by adults too.

This extended principle applies not only to mathematics but also to the teaching of other subjects. When designing curricula, teachers should take students' daily experiences into account and connect them with the knowledge being taught. For example, a science teacher can guide students in learning biology by observing plant growth, which not only increases students' learning motivation but also enables them to better grasp scientific concepts

The power of knowledge is reflected in many aspects. After mastering fundamental mathematical knowledge, children can apply this knowledge to solve problems in real life, such as calculating the cost of shopping or setting a budget when planning a trip. This practical utility makes learning mathematics more meaningful and enables children to think independently within society.

Furthermore, the Culturally Responsive Teaching (CRT) principle emphasizes that the knowledge students learn in the classroom should align with their cultural background. This means that educators should consider students' living environment and cultural differences to provide the most relevant learning content.

The process of learning mathematics is not just about memorizing formulas; more importantly, it involves cultivating the ability to solve problems. Through the study of Logo/Turtle Geometry, students can continuously reflect on and refine their methods through trial and error. This type of cognitive training is applicable not only to mathematics but also extends to various subjects, helping students to remain calm and apply their acquired knowledge to solve practical issues when facing difficulties in life.

• Can this problem be subdivided into simpler problems?
• Can this problem be related to a problem I already know how to solve?

In future articles, we will delve deeper into the specific applications of Logo/Turtle Geometry. Through the approach of 'Play Turtle. Do it yourself.,' we aim to enable more children to gain confidence and cultivate problem-solving abilities in this process. This will equip them to more confidently apply their knowledge and skills when facing future challenges. This is the authentic embodiment of Papert’s concept of 'Mindstorms' in modern education.