Lesson Ideas

These pages contain lesson ideas in various stages of development.

• Colored Sectors.  This activity helps young children distinguish the angle attribute from other attributes like area or length.  It involves designed manipulatives that I claim to be consistent with Montessori's manipulatives.  To see how I arrived at this design, click here.

• Fraction Circles and Polygons.  This activity teaches about external angles and prepares kids to draw polygons in Logo.

• The next three pages contain printable cards for use with Circular Reasoning.

  • Circular Reasoning Puzzle Cards.

  • Circular Reasoning Illustration Cards.

  • Circular Reasoning Vocabulary Cards.

• Cycloids.  Here's a NetLogo model that might be useful in teaching about cycloids.

You can also read about a fifteen hour class that raised performance levels of gifted 3rd graders above those of 8th and 12th graders on geometry questions from the National Assessment of Educational Progress.  The class was called Thinking About Circles and used Circular Reasoning software.

Bob Blodget (1998) told me about an intriguing computer-based exercise that he has used in Montessori classrooms to teach about the turtle turns associated with different regular polygons. I checked out the Logo Foundation web page, and found a paper called Research on Logo: Effects and Efficacy by Douglas Clements and Julie Meredith. One of the issues that they bring up is that mere exposure to Logo is not enough to increase math achievement. Clement and Meredith mention particular concepts that students need help with. One of these is the relationship between "turtle turn" and "angle measure." Also, student have trouble transfering Logo concepts to situations outside of Logo (e.g., high geometry).

So, inspired by Bob's design, I decided to try designing more computer-based, Montessori-type exercises that would help kids with issues. I tried to create writeups like the ones I did for my Montessori albums many years ago.  In each writeup, you will see typical sections found in Montessori albums (age, prerequisites, presentation, variations, extensions, points of interest, control of error, direct aims, and indirect aims).  I replaced the materials section with a section called screen objects.

I also added a couple of categories.  Software affordance describes the benefits of using software for the exercise, as opposed to concrete materials or some other medium like paper text documents or video tape.  Software constraints explains how software constrains manipulation of screen objects.  These constraints might be categorized by some as control of error, but since these are experimental activities, I wanted to explicitly separate constraints inherent in software designs because we need to consider whether these constraints are a help or a hindrance to children's work.

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