Month: August 2011

GeoGebra 4.0 Sneak Peek 9: Spreadsheet Improvements

GeoGebra

This is the 9th part of the GeoGebra 4.0 Sneak Peek series.  In this post, we are going to talk about the improvements made for the GeoGebra Spreadsheet view.

Spreadsheet is one feature of GeoGebra that is not found in other dynamic geometry software.  The spreadsheet enables us to have a numerical view of mathematical objects in addition to to the Algebra view and Graphics view.

In GeoGebra 4.0, the Spreadsheet view has its new set of tools as shown in the figure above.  The new tools include commands for basic matrix operations and basic statistics tools. Aside from these there are also other small improvements such as the autocomplete drop-down when you type commands.  » Read more

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Paper Folding: The proof of the cube root applet

High School Geometry

Last week, we have discussed the second part of our Paper Folding series, a fold that extracts the cube root of any number.   In this post, we are going to discuss its proof, but before that, let’s recall how to do the paper fold.

Paper Folding Instructions 

  1. Get a rectangular piece of paper and fold it in the middle, horizontally and vertically, and let the creases (see green segments in the applet) represent the coordinate axes.
  2. Let M denote (0,1) and let R denote (-r,0).
  3. Make a single fold that places M on y = -1 and R on x=r.
  4. The x-intercept of the fold is \sqrt[3]{r}.
The GeoGebra applet below visualizes the fold. Drag points P and Q to satisfy the conditions above. Note that you can also move point R.  » Read more
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When do mathematical definitions matter?

Pedagogy and Teaching

In the movie Hanna, Hanna was a 16 year old  girl who grew in the wilderness of Finland. Since two years old, she never had contact with the real world and modern technology.  Hanna learned about the world from Erik, his adopted father, and by reading books.  In one of the father-daughter conversations, Hannah asked about music. Their conversation was as follows.

Erik: Music is a combination of sounds with a view of beauty to form.
Hanna:  But how does it feel?
Erik: Good. It feels good. It’s, uh,nice.
Hanna:  Tell me properly. Can you play music?
Erik: Your mother could. She used to sing very well.
Hanna:  I’d like to hear it for myself.

Hanna probably feels the way students feel when we define an unfamiliar concept.  To students who are mathematically matured, definitions at the beginning of the lesson are probably understood, but for those who are just learning the basic concepts, it might be a little vague. Imagine a teacher saying that a function is a correspondence between two sets A and B, where each element in A has exactly one and only one corresponding element in B to students who have no prior experience of the said relationship.

» Read more

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