# Development of mathematical thinking - prevention of schematic Mathematics can not be reduced to the same accounting skills, this leads to blocking of.

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Development of mathematical thinking - prevention of schematic Mathematics can not be reduced to the same accounting skills, this leads to blocking of mathematical thinking. S. K. Stein

From the very beginning of education should focus on intellectual activity and independence of learners. Children should be encouraged to mathematical searching and reasoning, in line with their capabilities.

Drawing a spiral

string of numbers: 1, 1, 2, 2, 3, 3, 4, 4,...

Drawing a spiral string of numbers: 2, 1, 3, 2, 4, 3, 5, 4, 6, 5, 7,...

Paper cube I

Paper cube II

Mesh cube

Bio - blocks

front view left side view top view 4 1 2

Bio - blocks

Tower of Hanoi (1)

It consists of three rods, and a number of disks of different sizes which can slide onto any rod. The puzzle starts with the disks in a neat stack in ascending order of size on one rod, the smallest at the top, thus making a conical shape. Tower of Hanoi (2)

Tower of Hanoi (3)

Domino-based game

Picks theorem provides an elegant formula for the area of a simple lattice polygon: a lattice polygon whose boundary consists of a sequence of connected nonintersecting straight-line segments. Pick's theorem Georg Pick (1859-1942)

Lattice point Lattice point - the point where the two lines intersect forming a grid Picks formula

where: P - area of a polygon, W - the number of lattice points inside the polygon, B - number of lattice points on the edge of a polygon. Picks formula

A) B)C) Area of polygon lattice points on the edge B inside lattice points W A B C Picks formula

Using the Picks formula calculate polygonal areas

Picks formula

Fun on the perception How many squares you can get by connecting the dots with sections? 12461246

Example 1. 21 13 = 2 7 3 2 7 3 Cross-counting method