Of the nature of math and math in nature – a sequel about symmetry for children and adults

The original article was first published in the journal Mathematics and Informatics, issue 4, 2021, “Az-buki” national publisher . In this extended edition I add few more oibservations occured after article was published. There are additional questions for the readers.

Abstract. In this atricle I share a story about me, my children and their friends (aged 5 – 9 years) takiing part in activities for developing the notion of symmetries. Through play and active work we explored symmetries in sports, architecture, biology, language, music and mathematics. Most of the activities were carried out outdoors in nature. Few ideas for complementary activities with computers are presented.

I share couple of pedagogical principles for working with children:

  • learning trough multiple intelligences (as per Howard Gartner)
  • learning by making – students create things they can share with others
  • mistakes and challenges are considered as opportunities

As a result the children demonstrate the ability to recognize symmetries in areas and situations different from the ones set in the activities they performed. This proves the main thesis of the paper: the nature of mathematics can be captured successfully in an informal environment at any age.

Additional results

A month after our adventures with symmetry, the children’s interest led us to coding. In one of the activities, we learn to recognize notes written in Braille with our eyes closed. One of the children notices an interesting pattern. The notes symmetrically positioned on both sides of FA resemble each other. The last note, SI, is like the first note, DO, but flipped horizontally. The other pairs, RE-LA and MI-SOL, have the same property. It turns out that once we know about this pattern, we can learn only the first 4 notes and derive the rest symmetrically.

Symmetry helps us reduce the effort required for memorization.

More than 8 months have passed since the activities. The children continue to joyfully play some of the games we learned together. They remember them independently and spontaneously. Their favorite games are the tank game, creating rosettes, stars, and mandalas with the double mirror, and the mathematical constructor. We renamed the tank game to “Throwing Stones in the Puddle,” where instead of tanks, we draw puddles, and instead of projectiles, we throw stones.

In addition to noticing symmetry, the children have learned that learning brings joy and satisfaction. In their minds, the computer has become a tool for exploration, experimentation, writing, and sharing articles.

Tasks for reader-researchers

The meetings with the children continue, and every idea for a task in the spirit of exploration is welcome. Therefore, dear readers, you have the opportunity to share answers to the question “What tasks would you give to children with objects around them?” in the form below.

We explored symmetry with children in gymnastics, natural language, nature, music, mathematics, and more. It’s interesting for me to ponder, “In which other areas can we find symmetry?” For instance, does symmetry exist in human relationships, and if so, how does it manifest itself?

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