Showing posts with label distance formula. Show all posts
Showing posts with label distance formula. Show all posts

Tuesday, April 15, 2014

Angle Mouse and Other Scratch Geometry Projects

   Years ago I was asked to teach Benjamin Bloom's Taxonomy of Learning Domains to teachers. If I had to pick the one most important statement in the taxonomy it would be this; the ability to paraphrase is a test of comprehension. In other words, the more ways I can state a concept (paraphrase) the better I understand (comprehend) the concept.
   For example, consider the Distance Formula from analytic geometry.
   Is the ability to use the above formula in a Scratch program that computes the distance between an ant and the mouse-pointer a test of the programmer's comprehension  of the formula? That is, the Scratch program is a paraphrase of the distance formula. I've answered that question in the affirmative because I know how to express the formula in code that Scratch understands.
   Watch this short video that will hopefully convince you that the project is truly a paraphrase of the distance formula. As the mouse-pointer is moved, the distance between it and the ant is continuously updated.

   The Ant Chases the Mouse-pointer project can be viewed and downloaded at
   Here is a second example. This Scratch project is an effort to dynamically 'explain' the angle concept. The project is dynamic because it actually constructs the requested angle.

   This project can also be viewed and downloaded at the following link.
  Now a third and final example. This project is also dynamic in that it constructs the perpendicular to a point chosen at random on a line segment. Watch this short video.

   Click on this link to view or download the Perpendicular project.
   What do you think? Is programming (coding) a higher-level cognitive process than just memorizing a definition? As you can probably guess, I answered that question for myself a long time ago and I want learners, of all ages, to share the joy I experience when I successfully code a program.

Saturday, January 11, 2014

One Blind Mouse - An application of the Distance Formula

   In the previous post (The Distance Formula in Scratch, January 2014) I presented a tutorial on programming the distance formula from analytic geometry in Scratch.
   This Scratch project, One Blind Mouse, uses the distance formula to model how a blind mouse using its sense of smell can find a piece of cheese. The closer the mouse is to the cheeses, the stronger the smell and the farther away the mouse is from the cheese, the weaker the smell. Watch this very short video of the project.
   In the project, the algorithm causes the blind mouse to move over the plane, turning towards the cheese so as to continually shorten the distance between it and the cheese. When the red tip of the mouse's cane touches the cheese, the mouse has found it. Note that the mouse always spirals into the cheese even though 'spiral' is not in the code!
   You can view and download the project by clicking on this link.

Tuesday, January 7, 2014

The Distance Formula in Scratch

   I've written a short tutorial (in pdf format) that takes you step by step through the process of coding, in Scratch, the distance formula from analytic geometry.
   The tutorial follows the Algorithmic Thinking Model (see the December 2012 post, Algorithmic Thinking) that teaches that programming (or, to use the current term, coding) is a set of skills and not a single skill.
   View this short video that shows one of the Scratch scripts discussed in the tutorial. In the video, an ant chases a mouse-pointer as the pointer is moved around the screen. The distance between the ant and the mouse-pointer is computed using the distance formula.
   The script stops if the distance between the ant and the mouse-pointer is less than one.

   You can obtain a free copy of the Distance Formula Tutorial describing how to code the distance formula to create the script seen in the video by sending and email request to