This page supports trying new starts in math learning. That people can do math but think they can't, makes many unable to work with technical devices (e.g., computers).

Daily life uses numbers like twenty-four, twelve, sixty and three hundred sixty. Looking at them as in hours in a day (24), or examining the number of eggs in a cardboard carton (12, a dozen), minutes in an hour (60), and degrees in a complete rotation (360), can build numerical capabilities.

People often do things that have math background. They play card games, are active in sports, gamble, make health decisions, and do many other practical things (like buying insurance) that involve mathematics.

Items posted here could help kindle interest in starting math again. That is, learning in a less formal way.

Need for mathematical knowledge happens. That tells us we need learning activities in mathematics.

A rough idea of how to start such an activity begins in a recent paper^[15] latest version. Large numbers of topics and the cultures that gave rise to them appear at St. Andrews Math History Topics. The geometric questions that arise in an ancient puzzle are another possible start point.

There are many questions, I've considered: e.g., how to make an accurate approximation to one or another irrational number. For instance, to see how to do that for the base of natural logarithms got to e by powers.

Suppose you want to get started growing math capability. It could help if you were able to tell when some statement is plain wrong. Even when you're not sure which of two others is right, labeling the one that is wrong should get some credit. To do that use two diagrams reachable from clicking the link try.

The diagram on the left is in color. It shows six differently-shaded colored (blue, red and rose), three- (triangular) and four-sided (rectangular) regions.

The middle of the diagram at left has six corners; its shape and name follow

The Cuboctahedron is a very similar solid that was known to Archimedes. Like the image here it has "fourteen bases ... eight triangles". Instead of the Cuboctahedron's "six squares" the solid shown has that number of rectangles.

We could ask questions about these solids. In the image reached by the following link, try, the right diagram is black and white, with two kinds of lines, solid and dashed. The labeled points are each assigned one of the thirteen letters from a to m. The purpose is to allow a person to reflect what he or she believes regarding three simple statements characterizing a situation (like these solids).

If the light blue and light red regions were moved they and the light rose shape could make a six sided planar (lying in a flat plane) shape. Let's call the statement "Left figure has a six sided shape" the a label. (It is wrong, but if movement were allowed it could be right.) Let's call the statement "There are only triangular or three-sided and rectangular or four-sided regions in the colored part of the two diagrams," the b label. If c stands for "All the regions are three-sided in the colored part of the two diagrams," we know that is wrong but some people might not realize that.

Any answer on a line touching b (the correct answer) should get some credit. Any answer on a line between the two incorrect answers a and c should get nothing. Finally an answer of "I don't know," m should be rewarded somewhat (for honesty).

Links tagged with * show untraditional sources. Many are like this dancer: they move (are animated). Some speak. Others jump between topics or are unconventional beginnings. All could be part of offering new entry points to math. They are prototypes for using the world-wide web to enable re-entering the ideas of mathematics.

Italic links go to new items I've written. Other links are to student activities I've led. Others are things I've found on the web that could be worked into new K-12 class activities.