Children, Complexity, Abstraction and Infinity: How to Explain?

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Being a father of a 9-year-old and a 3-year-old, I’m fascinated about different methods to convey complex and abstract mathematical and scientific ideas to children of different ages. My pedagogical skills are tested on various topics ranging from the “shape of the universe“, to the concept of “dimensions”, negative numbers, and the concept of “zero” among other things.

Recently I’ve come across a video by Prof. Sean M. Carroll where he tries to explain the concept of dimensions to 5 different people; a child, a teen, a college student, a grad student, and an expert (the last one being more like a passive-aggressive dialogue between two physics professors as you might’ve guessed :):

Physicist Explains Dimensions in 5 Levels of Difficulty

When I mentioned this video to my wife, she said that she’s recently discovered a company whose name had something to do with 0 (Aleph zero) the concept of infinity, which, in turn, led to an an unexpected conversation on the topics of infinity (\infty ), cardinality of sets, cardinality of infinite sets, what it means to have different infinities, some of them “bigger” than the others. Inevitably, we ended up talking about the great mathematician Georg Cantor. Finally, my wife asked me the following question:

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How to describe the concept of zero to a 4-year-old?

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Two days ago, I and my 4-year-old son were having a great time together when he suddenly asked: “Daddy, what is zero?” Right in the middle of heavy physical play activity, I took a deep breath, and started to think about how I can describe the number zero to my son. The conversation went like the following: More

Do students who do their maths exercises on a tablet make more mistakes?

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According to a recent piece of news, the answer is a strong “yes”:

Students who do their maths exercises on a tablet make more mistakes, according to Stef Van Gorp, Master’s student at Thomas More University College in Mechelen, who examined the results of children in the third year of 16 primary schools. Van Gorp found that 72% of students make more mistakes on a tablet than on paper. On average, children made six mistakes on a tablet and just one on paper. Van Gorp’s conclusion was that children often consider tablets as toys and take the digital exercises less seriously. However, he said that mistakes can also be caused by the children not yet mastering the operation of a tablet.

tablet

You can read what Belgian newspapers said in Dutch here and here.

I have mixed feelings about this: Making mistakes is not a big deal, as long as children realize them in the process and learn from them. On the other hand, even though I’m all for bringing all of the advantages to education, I can’t stop myself from missing the robust nature of pencil, paper and huge black or white boards.

Impressions after completing the ‘How to Learn Math’ class

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The title of my blog entry for June 2, 2013 was “Can parents be better math teachers for their kids?“, referring to the online ‘How to Learn Math‘ class given by Prof.  Jo Boaler.  I had a few motivations for enrolling in this class, but the primary one was to get in touch with the latest methods and research in teaching mathematics. Even though I’m not a mathematics teacher by profession, I thought I could use the information and know-how I could gain for my son in the near future. I also had older kids in my extended family whom I tried to help in areas such as mathematics and programming.

This word cloud was generated on August 12th and is based on 5087 responses to the question "why do students often feel so bad about mistakes"?

This word cloud was generated on August 12th and is based on 5087 responses to the question “why do students often feel so bad about mistakes”?

Now that the class is over and I have completed it successfully, I can say that I’m satisfied with it more or less. One of the facts that Prof. Boaler admitted is that this was her first MOOC (Massive Open Online Course) experience, and I think next time she gives a similar class it will be better. I think some of the videos could be shorter, less repetitive, whereas some of the exercises could be a little more challenging, and structured, with more opportunities for valuable feedback. These points aside, it was very valuable to see the challenges faced by actual teachers, and listening to the experiences of students from diverse backgrounds were also helpful in developing a perspective. On top of that, some of my academic heroes, such as Sebastian Thrun, were there, providing me with very valuable insights with their interviews.

Once again I have seen that having a background in mathematics, engineering and cognitive science is not enough by itself to realize the better methods of teaching, and that is reason enough for me to be thankful to Jo Boaler for her continued efforts. I hope one day I will be good guide to my son and other kids in their journey to the wonderful world of sophisticated abstractions and surprising ideas with some unexpected connections 🙂

 

 

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